| {"family": "trig_chain", "expression": "cos(2*x**2 - x + 7)", "question": "Differentiate f(x) = cos(2*x**2 - x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(4*x - 1)*sin(2*x**2 - x + 7)"} | |
| {"family": "rational", "expression": "(-6*x - 4)/(6*x - 6)", "question": "Differentiate f(x) = (-6*x - 4)/(6*x - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-6*(-6*x - 4)/(6*x - 6)**2 - 6/(6*x - 6)"} | |
| {"family": "trig_chain", "expression": "cos(x**2 + 7*x - 5)", "question": "Differentiate f(x) = cos(x**2 + 7*x - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(2*x + 7)*sin(x**2 + 7*x - 5)"} | |
| {"family": "trig_chain", "expression": "-sin(5*x**2 + 3*x + 4)", "question": "Differentiate f(x) = -sin(5*x**2 + 3*x + 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(10*x + 3)*cos(5*x**2 + 3*x + 4)"} | |
| {"family": "power_chain", "expression": "(-5*x**2 - 3*x + 2)**2", "question": "Differentiate f(x) = (-5*x**2 - 3*x + 2)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-20*x - 6)*(-5*x**2 - 3*x + 2)"} | |
| {"family": "product_trig_chain", "expression": "(7*x + 5)*sin(2*x**2 + 9)", "question": "Differentiate f(x) = (7*x + 5)*sin(2*x**2 + 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*x*(7*x + 5)*cos(2*x**2 + 9) + 7*sin(2*x**2 + 9)"} | |
| {"family": "trig_chain", "expression": "sin(2*x**2 - x + 9)", "question": "Differentiate f(x) = sin(2*x**2 - x + 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(4*x - 1)*cos(2*x**2 - x + 9)"} | |
| {"family": "polynomial", "expression": "5*x**4 - 2*x**2 + 5*x - 6", "question": "Differentiate f(x) = 5*x**4 - 2*x**2 + 5*x - 6 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "20*x**3 - 4*x + 5"} | |
| {"family": "polynomial", "expression": "-6*x**4 + 5*x**2 - 4*x + 6", "question": "Differentiate f(x) = -6*x**4 + 5*x**2 - 4*x + 6 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-24*x**3 + 10*x - 4"} | |
| {"family": "product_trig_chain", "expression": "(4 - 4*x)*sin(4*x**2 - 9)", "question": "Differentiate f(x) = (4 - 4*x)*sin(4*x**2 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8*x*(4 - 4*x)*cos(4*x**2 - 9) - 4*sin(4*x**2 - 9)"} | |
| {"family": "product_trig_chain", "expression": "(-8*x - 4)*sin(5*x**2 + 3)", "question": "Differentiate f(x) = (-8*x - 4)*sin(5*x**2 + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x*(-8*x - 4)*cos(5*x**2 + 3) - 8*sin(5*x**2 + 3)"} | |
| {"family": "product", "expression": "(6 - 6*x**2)*(-x - 8)", "question": "Differentiate f(x) = (6 - 6*x**2)*(-x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x**2 - 12*x*(-x - 8) - 6"} | |
| {"family": "polynomial", "expression": "6*x**5 + 3*x**3 + 2*x + 2", "question": "Differentiate f(x) = 6*x**5 + 3*x**3 + 2*x + 2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "30*x**4 + 9*x**2 + 2"} | |
| {"family": "polynomial", "expression": "-5*x**5 - 2*x**3 + 8*x + 4", "question": "Differentiate f(x) = -5*x**5 - 2*x**3 + 8*x + 4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-25*x**4 - 6*x**2 + 8"} | |
| {"family": "rational", "expression": "(5 - 8*x)/(9*x + 5)", "question": "Differentiate f(x) = (5 - 8*x)/(9*x + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*(5 - 8*x)/(9*x + 5)**2 - 8/(9*x + 5)"} | |
| {"family": "product_trig_chain", "expression": "(8*x + 6)*(-sin(5*x**2 + 6))", "question": "Differentiate f(x) = (8*x + 6)*(-sin(5*x**2 + 6)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-10*x*(8*x + 6)*cos(5*x**2 + 6) - 8*sin(5*x**2 + 6)"} | |
| {"family": "product_trig_chain", "expression": "(5*x - 4)*sin(x**2 - 8)", "question": "Differentiate f(x) = (5*x - 4)*sin(x**2 - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "2*x*(5*x - 4)*cos(x**2 - 8) + 5*sin(x**2 - 8)"} | |
| {"family": "rational", "expression": "(8*x - 8)/(8 - 3*x)", "question": "Differentiate f(x) = (8*x - 8)/(8 - 3*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8/(8 - 3*x) + 3*(8*x - 8)/(8 - 3*x)**2"} | |
| {"family": "rational", "expression": "(9 - 5*x)/(9*x - 8)", "question": "Differentiate f(x) = (9 - 5*x)/(9*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*(9 - 5*x)/(9*x - 8)**2 - 5/(9*x - 8)"} | |
| {"family": "polynomial", "expression": "9*x**5 - 6*x**3 - 4*x - 9", "question": "Differentiate f(x) = 9*x**5 - 6*x**3 - 4*x - 9 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "45*x**4 - 18*x**2 - 4"} | |
| {"family": "product_trig_chain", "expression": "(5 - 2*x)*sin(2*x**2 + 3)", "question": "Differentiate f(x) = (5 - 2*x)*sin(2*x**2 + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*x*(5 - 2*x)*cos(2*x**2 + 3) - 2*sin(2*x**2 + 3)"} | |
| {"family": "product_trig_chain", "expression": "(9*x + 7)*sin(9*x**2 + 4)", "question": "Differentiate f(x) = (9*x + 7)*sin(9*x**2 + 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "18*x*(9*x + 7)*cos(9*x**2 + 4) + 9*sin(9*x**2 + 4)"} | |
| {"family": "product_trig_chain", "expression": "(2 - 9*x)*(-sin(4*x**2 - 6))", "question": "Differentiate f(x) = (2 - 9*x)*(-sin(4*x**2 - 6)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x*(2 - 9*x)*cos(4*x**2 - 6) + 9*sin(4*x**2 - 6)"} | |
| {"family": "product_trig_chain", "expression": "(-6*x - 9)*sin(4*x**2 + 8)", "question": "Differentiate f(x) = (-6*x - 9)*sin(4*x**2 + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8*x*(-6*x - 9)*cos(4*x**2 + 8) - 6*sin(4*x**2 + 8)"} | |
| {"family": "rational", "expression": "(5 - 8*x)/(4 - 5*x)", "question": "Differentiate f(x) = (5 - 8*x)/(4 - 5*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8/(4 - 5*x) + 5*(5 - 8*x)/(4 - 5*x)**2"} | |
| {"family": "product_trig_chain", "expression": "(-6*x - 9)*sin(3*x**2 + 1)", "question": "Differentiate f(x) = (-6*x - 9)*sin(3*x**2 + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x*(-6*x - 9)*cos(3*x**2 + 1) - 6*sin(3*x**2 + 1)"} | |
| {"family": "product_trig_chain", "expression": "(8 - 5*x)*(-sin(8*x**2 - 2))", "question": "Differentiate f(x) = (8 - 5*x)*(-sin(8*x**2 - 2)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-16*x*(8 - 5*x)*cos(8*x**2 - 2) + 5*sin(8*x**2 - 2)"} | |
| {"family": "product", "expression": "(-7*x - 1)*(-6*x**4 - 6)", "question": "Differentiate f(x) = (-7*x - 1)*(-6*x**4 - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "42*x**4 - 24*x**3*(-7*x - 1) + 42"} | |
| {"family": "polynomial", "expression": "6*x**4 + 4*x**2 + x - 7", "question": "Differentiate f(x) = 6*x**4 + 4*x**2 + x - 7 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "24*x**3 + 8*x + 1"} | |
| {"family": "product_trig_chain", "expression": "(6*x - 2)*sin(8*x**2 + 5)", "question": "Differentiate f(x) = (6*x - 2)*sin(8*x**2 + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "16*x*(6*x - 2)*cos(8*x**2 + 5) + 6*sin(8*x**2 + 5)"} | |
| {"family": "product", "expression": "(2 - 3*x)*(5*x**4 - 7)", "question": "Differentiate f(x) = (2 - 3*x)*(5*x**4 - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-15*x**4 + 20*x**3*(2 - 3*x) + 21"} | |
| {"family": "product_trig_chain", "expression": "(7*x + 6)*(-sin(5*x**2 - 1))", "question": "Differentiate f(x) = (7*x + 6)*(-sin(5*x**2 - 1)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-10*x*(7*x + 6)*cos(5*x**2 - 1) - 7*sin(5*x**2 - 1)"} | |
| {"family": "trig_chain", "expression": "-sin(9*x - 7)", "question": "Differentiate f(x) = -sin(9*x - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*cos(9*x - 7)"} | |
| {"family": "power_chain", "expression": "(9*x**2 + 7*x - 3)**4", "question": "Differentiate f(x) = (9*x**2 + 7*x - 3)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(72*x + 28)*(9*x**2 + 7*x - 3)**3"} | |
| {"family": "product_trig_chain", "expression": "(x + 9)*(-sin(9*x**2 + 9))", "question": "Differentiate f(x) = (x + 9)*(-sin(9*x**2 + 9)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-18*x*(x + 9)*cos(9*x**2 + 9) - sin(9*x**2 + 9)"} | |
| {"family": "rational", "expression": "(-2*x - 2)/(7 - 2*x)", "question": "Differentiate f(x) = (-2*x - 2)/(7 - 2*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2/(7 - 2*x) + 2*(-2*x - 2)/(7 - 2*x)**2"} | |
| {"family": "rational", "expression": "(3 - 3*x)/(2*x + 2)", "question": "Differentiate f(x) = (3 - 3*x)/(2*x + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2*(3 - 3*x)/(2*x + 2)**2 - 3/(2*x + 2)"} | |
| {"family": "trig_chain", "expression": "cos(4*x**2 + 8*x + 3)", "question": "Differentiate f(x) = cos(4*x**2 + 8*x + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(8*x + 8)*sin(4*x**2 + 8*x + 3)"} | |
| {"family": "power_chain", "expression": "(4*x**2 - 5*x - 3)**3", "question": "Differentiate f(x) = (4*x**2 - 5*x - 3)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(24*x - 15)*(4*x**2 - 5*x - 3)**2"} | |
| {"family": "product_trig_chain", "expression": "(6*x - 8)*sin(2*x**2 - 6)", "question": "Differentiate f(x) = (6*x - 8)*sin(2*x**2 - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*x*(6*x - 8)*cos(2*x**2 - 6) + 6*sin(2*x**2 - 6)"} | |
| {"family": "product_trig_chain", "expression": "(5*x - 1)*sin(x**2 + 2)", "question": "Differentiate f(x) = (5*x - 1)*sin(x**2 + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "2*x*(5*x - 1)*cos(x**2 + 2) + 5*sin(x**2 + 2)"} | |
| {"family": "power_chain", "expression": "(-4*x**2 - 3*x + 1)**3", "question": "Differentiate f(x) = (-4*x**2 - 3*x + 1)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-24*x - 9)*(-4*x**2 - 3*x + 1)**2"} | |
| {"family": "power_chain", "expression": "(-7*x**2 - 5*x + 2)**4", "question": "Differentiate f(x) = (-7*x**2 - 5*x + 2)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-56*x - 20)*(-7*x**2 - 5*x + 2)**3"} | |
| {"family": "power_chain", "expression": "(7*x**2 + 7*x - 5)**5", "question": "Differentiate f(x) = (7*x**2 + 7*x - 5)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(70*x + 35)*(7*x**2 + 7*x - 5)**4"} | |
| {"family": "product", "expression": "(9 - 7*x)*(x**4 + 3)", "question": "Differentiate f(x) = (9 - 7*x)*(x**4 + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-7*x**4 + 4*x**3*(9 - 7*x) - 21"} | |
| {"family": "product_trig_chain", "expression": "(8 - 8*x)*(-sin(5*x**2 - 9))", "question": "Differentiate f(x) = (8 - 8*x)*(-sin(5*x**2 - 9)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-10*x*(8 - 8*x)*cos(5*x**2 - 9) + 8*sin(5*x**2 - 9)"} | |
| {"family": "polynomial", "expression": "x**3 - 11*x - 3", "question": "Differentiate f(x) = x**3 - 11*x - 3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "3*x**2 - 11"} | |
| {"family": "product", "expression": "(-9*x - 7)*(-7*x**2 - 7)", "question": "Differentiate f(x) = (-9*x - 7)*(-7*x**2 - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "63*x**2 - 14*x*(-9*x - 7) + 63"} | |
| {"family": "power_chain", "expression": "(-6*x**2 + 8*x - 8)**4", "question": "Differentiate f(x) = (-6*x**2 + 8*x - 8)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(32 - 48*x)*(-6*x**2 + 8*x - 8)**3"} | |
| {"family": "product_trig_chain", "expression": "(-x - 5)*sin(x**2 - 1)", "question": "Differentiate f(x) = (-x - 5)*sin(x**2 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "2*x*(-x - 5)*cos(x**2 - 1) - sin(x**2 - 1)"} | |
| {"family": "product_trig_chain", "expression": "(-4*x - 2)*sin(6*x**2 - 1)", "question": "Differentiate f(x) = (-4*x - 2)*sin(6*x**2 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x*(-4*x - 2)*cos(6*x**2 - 1) - 4*sin(6*x**2 - 1)"} | |
| {"family": "rational", "expression": "(7 - x)/(4*x - 9)", "question": "Differentiate f(x) = (7 - x)/(4*x - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-4*(7 - x)/(4*x - 9)**2 - 1/(4*x - 9)"} | |
| {"family": "power_chain", "expression": "(-3*x**2 + 2*x - 2)**2", "question": "Differentiate f(x) = (-3*x**2 + 2*x - 2)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(4 - 12*x)*(-3*x**2 + 2*x - 2)"} | |
| {"family": "product_trig_chain", "expression": "(3*x - 6)*(-sin(6*x**2 + 2))", "question": "Differentiate f(x) = (3*x - 6)*(-sin(6*x**2 + 2)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x*(3*x - 6)*cos(6*x**2 + 2) - 3*sin(6*x**2 + 2)"} | |
| {"family": "product_trig_chain", "expression": "(2 - x)*sin(4*x**2 - 8)", "question": "Differentiate f(x) = (2 - x)*sin(4*x**2 - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8*x*(2 - x)*cos(4*x**2 - 8) - sin(4*x**2 - 8)"} | |
| {"family": "product", "expression": "(7 - 7*x)*(-2*x**3 - 5)", "question": "Differentiate f(x) = (7 - 7*x)*(-2*x**3 - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "14*x**3 - 6*x**2*(7 - 7*x) + 35"} | |
| {"family": "product_trig_chain", "expression": "(-3*x - 4)*sin(x**2 - 1)", "question": "Differentiate f(x) = (-3*x - 4)*sin(x**2 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "2*x*(-3*x - 4)*cos(x**2 - 1) - 3*sin(x**2 - 1)"} | |
| {"family": "product_trig_chain", "expression": "(8*x - 8)*(-sin(2*x**2 + 6))", "question": "Differentiate f(x) = (8*x - 8)*(-sin(2*x**2 + 6)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-4*x*(8*x - 8)*cos(2*x**2 + 6) - 8*sin(2*x**2 + 6)"} | |
| {"family": "product_trig_chain", "expression": "(x - 9)*(-sin(4*x**2 - 7))", "question": "Differentiate f(x) = (x - 9)*(-sin(4*x**2 - 7)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x*(x - 9)*cos(4*x**2 - 7) - sin(4*x**2 - 7)"} | |
| {"family": "product_trig_chain", "expression": "(3 - 9*x)*sin(2*x**2 - 2)", "question": "Differentiate f(x) = (3 - 9*x)*sin(2*x**2 - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*x*(3 - 9*x)*cos(2*x**2 - 2) - 9*sin(2*x**2 - 2)"} | |
| {"family": "product_trig_chain", "expression": "(4*x - 7)*sin(2*x**2 - 2)", "question": "Differentiate f(x) = (4*x - 7)*sin(2*x**2 - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*x*(4*x - 7)*cos(2*x**2 - 2) + 4*sin(2*x**2 - 2)"} | |
| {"family": "power_chain", "expression": "(-4*x**2 + 2*x - 7)**2", "question": "Differentiate f(x) = (-4*x**2 + 2*x - 7)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(4 - 16*x)*(-4*x**2 + 2*x - 7)"} | |
| {"family": "product_trig_chain", "expression": "(2*x + 7)*(-sin(8*x**2 + 8))", "question": "Differentiate f(x) = (2*x + 7)*(-sin(8*x**2 + 8)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-16*x*(2*x + 7)*cos(8*x**2 + 8) - 2*sin(8*x**2 + 8)"} | |
| {"family": "power_chain", "expression": "(-5*x**2 + 8*x + 8)**2", "question": "Differentiate f(x) = (-5*x**2 + 8*x + 8)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(16 - 20*x)*(-5*x**2 + 8*x + 8)"} | |
| {"family": "power_chain", "expression": "(7*x**2 - 6*x - 6)**5", "question": "Differentiate f(x) = (7*x**2 - 6*x - 6)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(70*x - 30)*(7*x**2 - 6*x - 6)**4"} | |
| {"family": "rational", "expression": "(-3*x - 3)/(7 - 6*x)", "question": "Differentiate f(x) = (-3*x - 3)/(7 - 6*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-3/(7 - 6*x) + 6*(-3*x - 3)/(7 - 6*x)**2"} | |
| {"family": "power_chain", "expression": "(7*x**2 + 3*x + 7)**2", "question": "Differentiate f(x) = (7*x**2 + 3*x + 7)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(28*x + 6)*(7*x**2 + 3*x + 7)"} | |
| {"family": "product_trig_chain", "expression": "(8 - 2*x)*(-sin(6*x**2 + 6))", "question": "Differentiate f(x) = (8 - 2*x)*(-sin(6*x**2 + 6)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x*(8 - 2*x)*cos(6*x**2 + 6) + 2*sin(6*x**2 + 6)"} | |
| {"family": "product", "expression": "(4*x - 7)*(7*x**4 + 3)", "question": "Differentiate f(x) = (4*x - 7)*(7*x**4 + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "28*x**4 + 28*x**3*(4*x - 7) + 12"} | |
| {"family": "product_trig_chain", "expression": "(x - 4)*sin(6*x**2 + 7)", "question": "Differentiate f(x) = (x - 4)*sin(6*x**2 + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x*(x - 4)*cos(6*x**2 + 7) + sin(6*x**2 + 7)"} | |
| {"family": "polynomial", "expression": "6*x**6 - x**4 - 6*x - 6", "question": "Differentiate f(x) = 6*x**6 - x**4 - 6*x - 6 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "36*x**5 - 4*x**3 - 6"} | |
| {"family": "trig_chain", "expression": "-sin(-9*x**2 + 9*x + 4)", "question": "Differentiate f(x) = -sin(-9*x**2 + 9*x + 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(9 - 18*x)*cos(-9*x**2 + 9*x + 4)"} | |
| {"family": "trig_chain", "expression": "-sin(x - 6)", "question": "Differentiate f(x) = -sin(x - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-cos(x - 6)"} | |
| {"family": "product", "expression": "(7*x - 4)*(5*x**2 - 8)", "question": "Differentiate f(x) = (7*x - 4)*(5*x**2 - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "35*x**2 + 10*x*(7*x - 4) - 56"} | |
| {"family": "product_trig_chain", "expression": "(7*x + 2)*sin(5*x**2 + 4)", "question": "Differentiate f(x) = (7*x + 2)*sin(5*x**2 + 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x*(7*x + 2)*cos(5*x**2 + 4) + 7*sin(5*x**2 + 4)"} | |
| {"family": "product_trig_chain", "expression": "(3*x + 4)*(-sin(8*x**2 - 4))", "question": "Differentiate f(x) = (3*x + 4)*(-sin(8*x**2 - 4)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-16*x*(3*x + 4)*cos(8*x**2 - 4) - 3*sin(8*x**2 - 4)"} | |
| {"family": "product", "expression": "(3*x + 2)*(-8*x**2 - 3)", "question": "Differentiate f(x) = (3*x + 2)*(-8*x**2 - 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-24*x**2 - 16*x*(3*x + 2) - 9"} | |
| {"family": "rational", "expression": "(8 - 2*x)/(-4*x - 5)", "question": "Differentiate f(x) = (8 - 2*x)/(-4*x - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*(8 - 2*x)/(-4*x - 5)**2 - 2/(-4*x - 5)"} | |
| {"family": "product_trig_chain", "expression": "(-3*x - 1)*(-sin(7*x**2 + 5))", "question": "Differentiate f(x) = (-3*x - 1)*(-sin(7*x**2 + 5)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-14*x*(-3*x - 1)*cos(7*x**2 + 5) + 3*sin(7*x**2 + 5)"} | |
| {"family": "rational", "expression": "(7*x - 1)/(9*x - 6)", "question": "Differentiate f(x) = (7*x - 1)/(9*x - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*(7*x - 1)/(9*x - 6)**2 + 7/(9*x - 6)"} | |
| {"family": "product_trig_chain", "expression": "(7*x + 8)*(-sin(6*x**2 - 1))", "question": "Differentiate f(x) = (7*x + 8)*(-sin(6*x**2 - 1)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x*(7*x + 8)*cos(6*x**2 - 1) - 7*sin(6*x**2 - 1)"} | |
| {"family": "rational", "expression": "(-2*x - 8)/(-9*x - 7)", "question": "Differentiate f(x) = (-2*x - 8)/(-9*x - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2/(-9*x - 7) + 9*(-2*x - 8)/(-9*x - 7)**2"} | |
| {"family": "product_trig_chain", "expression": "(5*x + 3)*(-sin(8*x**2 - 3))", "question": "Differentiate f(x) = (5*x + 3)*(-sin(8*x**2 - 3)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-16*x*(5*x + 3)*cos(8*x**2 - 3) - 5*sin(8*x**2 - 3)"} | |
| {"family": "power_chain", "expression": "(6*x**2 + 2*x + 1)**3", "question": "Differentiate f(x) = (6*x**2 + 2*x + 1)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(36*x + 6)*(6*x**2 + 2*x + 1)**2"} | |
| {"family": "product_trig_chain", "expression": "(-9*x - 4)*(-sin(4*x**2 - 6))", "question": "Differentiate f(x) = (-9*x - 4)*(-sin(4*x**2 - 6)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x*(-9*x - 4)*cos(4*x**2 - 6) + 9*sin(4*x**2 - 6)"} | |
| {"family": "product_trig_chain", "expression": "(-5*x - 8)*(-sin(8*x**2 - 5))", "question": "Differentiate f(x) = (-5*x - 8)*(-sin(8*x**2 - 5)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-16*x*(-5*x - 8)*cos(8*x**2 - 5) + 5*sin(8*x**2 - 5)"} | |
| {"family": "polynomial", "expression": "-2*x**4 + 2*x**2 - 3*x - 8", "question": "Differentiate f(x) = -2*x**4 + 2*x**2 - 3*x - 8 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x**3 + 4*x - 3"} | |
| {"family": "polynomial", "expression": "x**4 - 4*x**2 - 7*x + 7", "question": "Differentiate f(x) = x**4 - 4*x**2 - 7*x + 7 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*x**3 - 8*x - 7"} | |
| {"family": "product_trig_chain", "expression": "(-4*x - 1)*sin(6*x**2 - 1)", "question": "Differentiate f(x) = (-4*x - 1)*sin(6*x**2 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x*(-4*x - 1)*cos(6*x**2 - 1) - 4*sin(6*x**2 - 1)"} | |
| {"family": "product_trig_chain", "expression": "(-9*x - 2)*sin(7*x**2 - 4)", "question": "Differentiate f(x) = (-9*x - 2)*sin(7*x**2 - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "14*x*(-9*x - 2)*cos(7*x**2 - 4) - 9*sin(7*x**2 - 4)"} | |
| {"family": "trig_chain", "expression": "sin(2*x + 4)", "question": "Differentiate f(x) = sin(2*x + 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "2*cos(2*x + 4)"} | |
| {"family": "power_chain", "expression": "(-2*x**2 - x - 7)**4", "question": "Differentiate f(x) = (-2*x**2 - x - 7)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-16*x - 4)*(-2*x**2 - x - 7)**3"} | |
| {"family": "polynomial", "expression": "-2*x**4 - 6*x**2 - x - 1", "question": "Differentiate f(x) = -2*x**4 - 6*x**2 - x - 1 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x**3 - 12*x - 1"} | |
| {"family": "product_trig_chain", "expression": "(9*x + 6)*sin(4*x**2 + 7)", "question": "Differentiate f(x) = (9*x + 6)*sin(4*x**2 + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8*x*(9*x + 6)*cos(4*x**2 + 7) + 9*sin(4*x**2 + 7)"} | |
| {"family": "rational", "expression": "(6 - 6*x)/(-7*x - 9)", "question": "Differentiate f(x) = (6 - 6*x)/(-7*x - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "7*(6 - 6*x)/(-7*x - 9)**2 - 6/(-7*x - 9)"} | |
| {"family": "rational", "expression": "(-5*x - 1)/(8*x + 1)", "question": "Differentiate f(x) = (-5*x - 1)/(8*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*(-5*x - 1)/(8*x + 1)**2 - 5/(8*x + 1)"} | |
| {"family": "trig_chain", "expression": "sin(4*x - 4)", "question": "Differentiate f(x) = sin(4*x - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*cos(4*x - 4)"} | |
| {"family": "power_chain", "expression": "(x**2 + 8*x - 1)**5", "question": "Differentiate f(x) = (x**2 + 8*x - 1)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(10*x + 40)*(x**2 + 8*x - 1)**4"} | |
| {"family": "product", "expression": "(6 - 2*x**3)*(x + 6)", "question": "Differentiate f(x) = (6 - 2*x**3)*(x + 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2*x**3 - 6*x**2*(x + 6) + 6"} | |
| {"family": "product_trig_chain", "expression": "(4 - 9*x)*sin(x**2 + 9)", "question": "Differentiate f(x) = (4 - 9*x)*sin(x**2 + 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "2*x*(4 - 9*x)*cos(x**2 + 9) - 9*sin(x**2 + 9)"} | |
| {"family": "product", "expression": "(6*x - 5)*(7*x**4 - 9)", "question": "Differentiate f(x) = (6*x - 5)*(7*x**4 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "42*x**4 + 28*x**3*(6*x - 5) - 54"} | |
| {"family": "trig_chain", "expression": "-sin(7*x**2 + 6*x + 8)", "question": "Differentiate f(x) = -sin(7*x**2 + 6*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(14*x + 6)*cos(7*x**2 + 6*x + 8)"} | |
| {"family": "rational", "expression": "(8*x - 1)/(4 - 2*x)", "question": "Differentiate f(x) = (8*x - 1)/(4 - 2*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8/(4 - 2*x) + 2*(8*x - 1)/(4 - 2*x)**2"} | |
| {"family": "product_trig_chain", "expression": "(x + 4)*sin(8*x**2 - 3)", "question": "Differentiate f(x) = (x + 4)*sin(8*x**2 - 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "16*x*(x + 4)*cos(8*x**2 - 3) + sin(8*x**2 - 3)"} | |
| {"family": "polynomial", "expression": "-6*x**3 + 13*x + 4", "question": "Differentiate f(x) = -6*x**3 + 13*x + 4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "13 - 18*x**2"} | |
| {"family": "product_trig_chain", "expression": "(7*x - 9)*(-sin(8*x**2 + 9))", "question": "Differentiate f(x) = (7*x - 9)*(-sin(8*x**2 + 9)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-16*x*(7*x - 9)*cos(8*x**2 + 9) - 7*sin(8*x**2 + 9)"} | |
| {"family": "power_chain", "expression": "(-5*x**2 - 6*x - 3)**4", "question": "Differentiate f(x) = (-5*x**2 - 6*x - 3)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-40*x - 24)*(-5*x**2 - 6*x - 3)**3"} | |
| {"family": "power_chain", "expression": "(-6*x**2 - 6*x - 8)**4", "question": "Differentiate f(x) = (-6*x**2 - 6*x - 8)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-48*x - 24)*(-6*x**2 - 6*x - 8)**3"} | |
| {"family": "product_trig_chain", "expression": "(4*x - 3)*(-sin(7*x**2 + 4))", "question": "Differentiate f(x) = (4*x - 3)*(-sin(7*x**2 + 4)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-14*x*(4*x - 3)*cos(7*x**2 + 4) - 4*sin(7*x**2 + 4)"} | |
| {"family": "product_trig_chain", "expression": "(x - 3)*sin(5*x**2 - 3)", "question": "Differentiate f(x) = (x - 3)*sin(5*x**2 - 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x*(x - 3)*cos(5*x**2 - 3) + sin(5*x**2 - 3)"} | |
| {"family": "product_trig_chain", "expression": "(-2*x - 1)*(-sin(5*x**2 + 6))", "question": "Differentiate f(x) = (-2*x - 1)*(-sin(5*x**2 + 6)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-10*x*(-2*x - 1)*cos(5*x**2 + 6) + 2*sin(5*x**2 + 6)"} | |
| {"family": "product", "expression": "(4 - 2*x)*(-6*x**4 - 7)", "question": "Differentiate f(x) = (4 - 2*x)*(-6*x**4 - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x**4 - 24*x**3*(4 - 2*x) + 14"} | |
| {"family": "product_trig_chain", "expression": "(8 - 4*x)*(-sin(x**2 - 4))", "question": "Differentiate f(x) = (8 - 4*x)*(-sin(x**2 - 4)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2*x*(8 - 4*x)*cos(x**2 - 4) + 4*sin(x**2 - 4)"} | |
| {"family": "product_trig_chain", "expression": "(-2*x - 9)*sin(x**2 - 1)", "question": "Differentiate f(x) = (-2*x - 9)*sin(x**2 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "2*x*(-2*x - 9)*cos(x**2 - 1) - 2*sin(x**2 - 1)"} | |
| {"family": "product_trig_chain", "expression": "(-4*x - 4)*sin(8*x**2 - 4)", "question": "Differentiate f(x) = (-4*x - 4)*sin(8*x**2 - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "16*x*(-4*x - 4)*cos(8*x**2 - 4) - 4*sin(8*x**2 - 4)"} | |
| {"family": "rational", "expression": "(x - 6)/(6*x - 6)", "question": "Differentiate f(x) = (x - 6)/(6*x - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-6*(x - 6)/(6*x - 6)**2 + 1/(6*x - 6)"} | |
| {"family": "rational", "expression": "(3*x + 4)/(3 - 6*x)", "question": "Differentiate f(x) = (3*x + 4)/(3 - 6*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "3/(3 - 6*x) + 6*(3*x + 4)/(3 - 6*x)**2"} | |
| {"family": "product_trig_chain", "expression": "(1 - 7*x)*(-sin(3*x**2 - 3))", "question": "Differentiate f(x) = (1 - 7*x)*(-sin(3*x**2 - 3)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-6*x*(1 - 7*x)*cos(3*x**2 - 3) + 7*sin(3*x**2 - 3)"} | |
| {"family": "rational", "expression": "(-5*x - 5)/(8*x - 1)", "question": "Differentiate f(x) = (-5*x - 5)/(8*x - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*(-5*x - 5)/(8*x - 1)**2 - 5/(8*x - 1)"} | |
| {"family": "trig_chain", "expression": "cos(8*x**2 + 6*x + 2)", "question": "Differentiate f(x) = cos(8*x**2 + 6*x + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(16*x + 6)*sin(8*x**2 + 6*x + 2)"} | |
| {"family": "polynomial", "expression": "-2*x**4 + 7*x**2 - 3*x + 7", "question": "Differentiate f(x) = -2*x**4 + 7*x**2 - 3*x + 7 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x**3 + 14*x - 3"} | |
| {"family": "power_chain", "expression": "(-3*x**2 - 8*x + 3)**2", "question": "Differentiate f(x) = (-3*x**2 - 8*x + 3)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-12*x - 16)*(-3*x**2 - 8*x + 3)"} | |
| {"family": "polynomial", "expression": "-x**4 + 6*x**2 - 5*x + 5", "question": "Differentiate f(x) = -x**4 + 6*x**2 - 5*x + 5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-4*x**3 + 12*x - 5"} | |
| {"family": "product", "expression": "(x + 5)*(-9*x**4 - 2)", "question": "Differentiate f(x) = (x + 5)*(-9*x**4 - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*x**4 - 36*x**3*(x + 5) - 2"} | |
| {"family": "product", "expression": "(4 - 3*x)*(-6*x**4 - 9)", "question": "Differentiate f(x) = (4 - 3*x)*(-6*x**4 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "18*x**4 - 24*x**3*(4 - 3*x) + 27"} | |
| {"family": "product_trig_chain", "expression": "(x + 4)*(-sin(7*x**2 + 5))", "question": "Differentiate f(x) = (x + 4)*(-sin(7*x**2 + 5)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-14*x*(x + 4)*cos(7*x**2 + 5) - sin(7*x**2 + 5)"} | |
| {"family": "product", "expression": "(x + 5)*(7*x**3 - 9)", "question": "Differentiate f(x) = (x + 5)*(7*x**3 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "7*x**3 + 21*x**2*(x + 5) - 9"} | |
| {"family": "power_chain", "expression": "(-5*x**2 + 6*x - 3)**4", "question": "Differentiate f(x) = (-5*x**2 + 6*x - 3)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(24 - 40*x)*(-5*x**2 + 6*x - 3)**3"} | |
| {"family": "product", "expression": "(6*x - 5)*(8*x**3 + 3)", "question": "Differentiate f(x) = (6*x - 5)*(8*x**3 + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "48*x**3 + 24*x**2*(6*x - 5) + 18"} | |
| {"family": "product_trig_chain", "expression": "(9*x - 1)*(-sin(4*x**2 + 5))", "question": "Differentiate f(x) = (9*x - 1)*(-sin(4*x**2 + 5)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x*(9*x - 1)*cos(4*x**2 + 5) - 9*sin(4*x**2 + 5)"} | |
| {"family": "product", "expression": "(7 - 3*x**3)*(9 - 7*x)", "question": "Differentiate f(x) = (7 - 3*x**3)*(9 - 7*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "21*x**3 - 9*x**2*(9 - 7*x) - 49"} | |
| {"family": "rational", "expression": "(3*x - 4)/(-5*x - 5)", "question": "Differentiate f(x) = (3*x - 4)/(-5*x - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "3/(-5*x - 5) + 5*(3*x - 4)/(-5*x - 5)**2"} | |
| {"family": "product_trig_chain", "expression": "(9 - 3*x)*sin(6*x**2 - 5)", "question": "Differentiate f(x) = (9 - 3*x)*sin(6*x**2 - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x*(9 - 3*x)*cos(6*x**2 - 5) - 3*sin(6*x**2 - 5)"} | |
| {"family": "polynomial", "expression": "3*x**5 - 3*x**3 - 6*x - 3", "question": "Differentiate f(x) = 3*x**5 - 3*x**3 - 6*x - 3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "15*x**4 - 9*x**2 - 6"} | |
| {"family": "product", "expression": "(-9*x - 1)*(-8*x**3 - 1)", "question": "Differentiate f(x) = (-9*x - 1)*(-8*x**3 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "72*x**3 - 24*x**2*(-9*x - 1) + 9"} | |
| {"family": "product_trig_chain", "expression": "(5*x + 6)*sin(6*x**2 - 1)", "question": "Differentiate f(x) = (5*x + 6)*sin(6*x**2 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x*(5*x + 6)*cos(6*x**2 - 1) + 5*sin(6*x**2 - 1)"} | |
| {"family": "power_chain", "expression": "(2*x**2 + 9*x - 6)**3", "question": "Differentiate f(x) = (2*x**2 + 9*x - 6)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(12*x + 27)*(2*x**2 + 9*x - 6)**2"} | |
| {"family": "product", "expression": "(3*x - 3)*(-5*x**4 - 9)", "question": "Differentiate f(x) = (3*x - 3)*(-5*x**4 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-15*x**4 - 20*x**3*(3*x - 3) - 27"} | |
| {"family": "polynomial", "expression": "8*x**5 + 6*x**3 - 3*x - 4", "question": "Differentiate f(x) = 8*x**5 + 6*x**3 - 3*x - 4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "40*x**4 + 18*x**2 - 3"} | |
| {"family": "trig_chain", "expression": "cos(2*x**2 - 2*x + 1)", "question": "Differentiate f(x) = cos(2*x**2 - 2*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(4*x - 2)*sin(2*x**2 - 2*x + 1)"} | |
| {"family": "rational", "expression": "(5 - 9*x)/(-3*x - 5)", "question": "Differentiate f(x) = (5 - 9*x)/(-3*x - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "3*(5 - 9*x)/(-3*x - 5)**2 - 9/(-3*x - 5)"} | |
| {"family": "polynomial", "expression": "x**5 - 9*x**3 + 3*x + 7", "question": "Differentiate f(x) = x**5 - 9*x**3 + 3*x + 7 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "5*x**4 - 27*x**2 + 3"} | |
| {"family": "product_trig_chain", "expression": "(-2*x - 5)*(-sin(x**2 - 7))", "question": "Differentiate f(x) = (-2*x - 5)*(-sin(x**2 - 7)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2*x*(-2*x - 5)*cos(x**2 - 7) + 2*sin(x**2 - 7)"} | |
| {"family": "product_trig_chain", "expression": "(2 - 7*x)*(-sin(6*x**2 - 7))", "question": "Differentiate f(x) = (2 - 7*x)*(-sin(6*x**2 - 7)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x*(2 - 7*x)*cos(6*x**2 - 7) + 7*sin(6*x**2 - 7)"} | |
| {"family": "trig_chain", "expression": "cos(-6*x**2 + 8*x + 9)", "question": "Differentiate f(x) = cos(-6*x**2 + 8*x + 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(8 - 12*x)*sin(-6*x**2 + 8*x + 9)"} | |
| {"family": "trig_chain", "expression": "sin(4*x + 1)", "question": "Differentiate f(x) = sin(4*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*cos(4*x + 1)"} | |
| {"family": "trig_chain", "expression": "-sin(-9*x**2 + 3*x + 1)", "question": "Differentiate f(x) = -sin(-9*x**2 + 3*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(3 - 18*x)*cos(-9*x**2 + 3*x + 1)"} | |
| {"family": "product", "expression": "(1 - 7*x)*(9*x**2 + 2)", "question": "Differentiate f(x) = (1 - 7*x)*(9*x**2 + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-63*x**2 + 18*x*(1 - 7*x) - 14"} | |
| {"family": "rational", "expression": "(x - 7)/(-2*x - 7)", "question": "Differentiate f(x) = (x - 7)/(-2*x - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "1/(-2*x - 7) + 2*(x - 7)/(-2*x - 7)**2"} | |
| {"family": "product", "expression": "(-x - 7)*(7*x**3 + 1)", "question": "Differentiate f(x) = (-x - 7)*(7*x**3 + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-7*x**3 + 21*x**2*(-x - 7) - 1"} | |
| {"family": "product_trig_chain", "expression": "(9*x - 5)*(-sin(6*x**2 - 3))", "question": "Differentiate f(x) = (9*x - 5)*(-sin(6*x**2 - 3)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x*(9*x - 5)*cos(6*x**2 - 3) - 9*sin(6*x**2 - 3)"} | |
| {"family": "polynomial", "expression": "-5*x**5 - 5*x**3 + 7*x - 5", "question": "Differentiate f(x) = -5*x**5 - 5*x**3 + 7*x - 5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-25*x**4 - 15*x**2 + 7"} | |
| {"family": "product_trig_chain", "expression": "(5 - 5*x)*sin(5*x**2 - 1)", "question": "Differentiate f(x) = (5 - 5*x)*sin(5*x**2 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x*(5 - 5*x)*cos(5*x**2 - 1) - 5*sin(5*x**2 - 1)"} | |
| {"family": "trig_chain", "expression": "cos(2*x - 7)", "question": "Differentiate f(x) = cos(2*x - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2*sin(2*x - 7)"} | |
| {"family": "product_trig_chain", "expression": "(6*x + 3)*(-sin(7*x**2 + 3))", "question": "Differentiate f(x) = (6*x + 3)*(-sin(7*x**2 + 3)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-14*x*(6*x + 3)*cos(7*x**2 + 3) - 6*sin(7*x**2 + 3)"} | |
| {"family": "product_trig_chain", "expression": "(6 - 4*x)*sin(6*x**2 + 6)", "question": "Differentiate f(x) = (6 - 4*x)*sin(6*x**2 + 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x*(6 - 4*x)*cos(6*x**2 + 6) - 4*sin(6*x**2 + 6)"} | |
| {"family": "polynomial", "expression": "x**6 + x**4 + 7*x + 5", "question": "Differentiate f(x) = x**6 + x**4 + 7*x + 5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x**5 + 4*x**3 + 7"} | |
| {"family": "product", "expression": "(9*x + 5)*(6*x**4 - 9)", "question": "Differentiate f(x) = (9*x + 5)*(6*x**4 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "54*x**4 + 24*x**3*(9*x + 5) - 81"} | |
| {"family": "trig_chain", "expression": "cos(5*x + 5)", "question": "Differentiate f(x) = cos(5*x + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-5*sin(5*x + 5)"} | |
| {"family": "product_trig_chain", "expression": "(2*x - 2)*sin(4*x**2 - 2)", "question": "Differentiate f(x) = (2*x - 2)*sin(4*x**2 - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8*x*(2*x - 2)*cos(4*x**2 - 2) + 2*sin(4*x**2 - 2)"} | |
| {"family": "power_chain", "expression": "(6*x**2 - 5*x + 2)**3", "question": "Differentiate f(x) = (6*x**2 - 5*x + 2)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(36*x - 15)*(6*x**2 - 5*x + 2)**2"} | |
| {"family": "product_trig_chain", "expression": "(9 - 9*x)*sin(5*x**2 + 8)", "question": "Differentiate f(x) = (9 - 9*x)*sin(5*x**2 + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x*(9 - 9*x)*cos(5*x**2 + 8) - 9*sin(5*x**2 + 8)"} | |
| {"family": "product", "expression": "(6 - 5*x)*(-8*x**3 - 9)", "question": "Differentiate f(x) = (6 - 5*x)*(-8*x**3 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "40*x**3 - 24*x**2*(6 - 5*x) + 45"} | |
| {"family": "product_trig_chain", "expression": "(7 - 3*x)*sin(5*x**2 - 2)", "question": "Differentiate f(x) = (7 - 3*x)*sin(5*x**2 - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x*(7 - 3*x)*cos(5*x**2 - 2) - 3*sin(5*x**2 - 2)"} | |
| {"family": "rational", "expression": "(4*x - 6)/(-6*x - 2)", "question": "Differentiate f(x) = (4*x - 6)/(-6*x - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4/(-6*x - 2) + 6*(4*x - 6)/(-6*x - 2)**2"} | |
| {"family": "rational", "expression": "(2 - 3*x)/(7 - 9*x)", "question": "Differentiate f(x) = (2 - 3*x)/(7 - 9*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9*(2 - 3*x)/(7 - 9*x)**2 - 3/(7 - 9*x)"} | |
| {"family": "product_trig_chain", "expression": "(x - 8)*sin(5*x**2 + 5)", "question": "Differentiate f(x) = (x - 8)*sin(5*x**2 + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x*(x - 8)*cos(5*x**2 + 5) + sin(5*x**2 + 5)"} | |
| {"family": "product_trig_chain", "expression": "(-3*x - 8)*sin(8*x**2 - 9)", "question": "Differentiate f(x) = (-3*x - 8)*sin(8*x**2 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "16*x*(-3*x - 8)*cos(8*x**2 - 9) - 3*sin(8*x**2 - 9)"} | |
| {"family": "rational", "expression": "(x - 7)/(4 - x)", "question": "Differentiate f(x) = (x - 7)/(4 - x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "1/(4 - x) + (x - 7)/(4 - x)**2"} | |
| {"family": "polynomial", "expression": "2*x**3 - 3*x - 1", "question": "Differentiate f(x) = 2*x**3 - 3*x - 1 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x**2 - 3"} | |
| {"family": "product", "expression": "(6 - 7*x**4)*(7 - 3*x)", "question": "Differentiate f(x) = (6 - 7*x**4)*(7 - 3*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "21*x**4 - 28*x**3*(7 - 3*x) - 18"} | |
| {"family": "power_chain", "expression": "(-6*x**2 - 4*x + 1)**3", "question": "Differentiate f(x) = (-6*x**2 - 4*x + 1)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-36*x - 12)*(-6*x**2 - 4*x + 1)**2"} | |
| {"family": "trig_chain", "expression": "sin(-9*x**2 + 7*x + 1)", "question": "Differentiate f(x) = sin(-9*x**2 + 7*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(7 - 18*x)*cos(-9*x**2 + 7*x + 1)"} | |
| {"family": "trig_chain", "expression": "-sin(4*x**2 - 4*x + 9)", "question": "Differentiate f(x) = -sin(4*x**2 - 4*x + 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(8*x - 4)*cos(4*x**2 - 4*x + 9)"} | |
| {"family": "rational", "expression": "(-8*x - 9)/(-4*x - 4)", "question": "Differentiate f(x) = (-8*x - 9)/(-4*x - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*(-8*x - 9)/(-4*x - 4)**2 - 8/(-4*x - 4)"} | |
| {"family": "product_trig_chain", "expression": "(8*x + 4)*sin(7*x**2 - 7)", "question": "Differentiate f(x) = (8*x + 4)*sin(7*x**2 - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "14*x*(8*x + 4)*cos(7*x**2 - 7) + 8*sin(7*x**2 - 7)"} | |
| {"family": "polynomial", "expression": "3*x**6 + 3*x**4 + 9*x - 9", "question": "Differentiate f(x) = 3*x**6 + 3*x**4 + 9*x - 9 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "18*x**5 + 12*x**3 + 9"} | |
| {"family": "product", "expression": "(6*x - 6)*(5*x**3 - 5)", "question": "Differentiate f(x) = (6*x - 6)*(5*x**3 - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "30*x**3 + 15*x**2*(6*x - 6) - 30"} | |
| {"family": "power_chain", "expression": "(-7*x**2 + 8*x - 3)**5", "question": "Differentiate f(x) = (-7*x**2 + 8*x - 3)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(40 - 70*x)*(-7*x**2 + 8*x - 3)**4"} | |
| {"family": "polynomial", "expression": "4*x**6 + 2*x**4 + 2*x + 5", "question": "Differentiate f(x) = 4*x**6 + 2*x**4 + 2*x + 5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "24*x**5 + 8*x**3 + 2"} | |
| {"family": "power_chain", "expression": "(-9*x**2 + 7*x - 1)**2", "question": "Differentiate f(x) = (-9*x**2 + 7*x - 1)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(14 - 36*x)*(-9*x**2 + 7*x - 1)"} | |
| {"family": "product", "expression": "(1 - 5*x**3)*(8 - 5*x)", "question": "Differentiate f(x) = (1 - 5*x**3)*(8 - 5*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "25*x**3 - 15*x**2*(8 - 5*x) - 5"} | |
| {"family": "polynomial", "expression": "2*x**3 - 10*x - 7", "question": "Differentiate f(x) = 2*x**3 - 10*x - 7 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x**2 - 10"} | |
| {"family": "product_trig_chain", "expression": "(-x - 3)*sin(3*x**2 + 3)", "question": "Differentiate f(x) = (-x - 3)*sin(3*x**2 + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x*(-x - 3)*cos(3*x**2 + 3) - sin(3*x**2 + 3)"} | |
| {"family": "trig_chain", "expression": "sin(7*x**2 + 2*x + 7)", "question": "Differentiate f(x) = sin(7*x**2 + 2*x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(14*x + 2)*cos(7*x**2 + 2*x + 7)"} | |
| {"family": "polynomial", "expression": "4*x**6 + 8*x**4 - 9*x - 4", "question": "Differentiate f(x) = 4*x**6 + 8*x**4 - 9*x - 4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "24*x**5 + 32*x**3 - 9"} | |
| {"family": "polynomial", "expression": "9*x**5 + 2*x**3 + 4*x - 2", "question": "Differentiate f(x) = 9*x**5 + 2*x**3 + 4*x - 2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "45*x**4 + 6*x**2 + 4"} | |
| {"family": "trig_chain", "expression": "cos(2*x**2 - 4*x + 3)", "question": "Differentiate f(x) = cos(2*x**2 - 4*x + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(4*x - 4)*sin(2*x**2 - 4*x + 3)"} | |
| {"family": "polynomial", "expression": "5*x**4 - 8*x**2 - 6*x - 6", "question": "Differentiate f(x) = 5*x**4 - 8*x**2 - 6*x - 6 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "20*x**3 - 16*x - 6"} | |
| {"family": "product_trig_chain", "expression": "(5*x + 4)*(-sin(7*x**2 - 7))", "question": "Differentiate f(x) = (5*x + 4)*(-sin(7*x**2 - 7)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-14*x*(5*x + 4)*cos(7*x**2 - 7) - 5*sin(7*x**2 - 7)"} | |
| {"family": "product_trig_chain", "expression": "(9 - 3*x)*sin(5*x**2 + 1)", "question": "Differentiate f(x) = (9 - 3*x)*sin(5*x**2 + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x*(9 - 3*x)*cos(5*x**2 + 1) - 3*sin(5*x**2 + 1)"} | |
| {"family": "power_chain", "expression": "(-5*x**2 + 7*x + 7)**2", "question": "Differentiate f(x) = (-5*x**2 + 7*x + 7)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(14 - 20*x)*(-5*x**2 + 7*x + 7)"} | |
| {"family": "power_chain", "expression": "(6*x**2 - 4*x + 1)**5", "question": "Differentiate f(x) = (6*x**2 - 4*x + 1)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(60*x - 20)*(6*x**2 - 4*x + 1)**4"} | |
| {"family": "product", "expression": "(9*x - 6)*(5*x**4 - 7)", "question": "Differentiate f(x) = (9*x - 6)*(5*x**4 - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "45*x**4 + 20*x**3*(9*x - 6) - 63"} | |
| {"family": "trig_chain", "expression": "cos(8*x + 4)", "question": "Differentiate f(x) = cos(8*x + 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*sin(8*x + 4)"} | |
| {"family": "polynomial", "expression": "-4*x**4 - 7*x**2 - 5*x - 2", "question": "Differentiate f(x) = -4*x**4 - 7*x**2 - 5*x - 2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-16*x**3 - 14*x - 5"} | |
| {"family": "power_chain", "expression": "(5*x**2 + x - 4)**4", "question": "Differentiate f(x) = (5*x**2 + x - 4)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(40*x + 4)*(5*x**2 + x - 4)**3"} | |
| {"family": "product_trig_chain", "expression": "(x - 3)*sin(4*x**2 - 1)", "question": "Differentiate f(x) = (x - 3)*sin(4*x**2 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8*x*(x - 3)*cos(4*x**2 - 1) + sin(4*x**2 - 1)"} | |
| {"family": "polynomial", "expression": "-8*x**6 - x**4 - 5*x - 8", "question": "Differentiate f(x) = -8*x**6 - x**4 - 5*x - 8 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-48*x**5 - 4*x**3 - 5"} | |
| {"family": "product_trig_chain", "expression": "(5 - 6*x)*sin(2*x**2 + 7)", "question": "Differentiate f(x) = (5 - 6*x)*sin(2*x**2 + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*x*(5 - 6*x)*cos(2*x**2 + 7) - 6*sin(2*x**2 + 7)"} | |
| {"family": "trig_chain", "expression": "cos(5*x**2 + 3*x - 6)", "question": "Differentiate f(x) = cos(5*x**2 + 3*x - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(10*x + 3)*sin(5*x**2 + 3*x - 6)"} | |
| {"family": "product_trig_chain", "expression": "(4*x - 5)*sin(7*x**2 + 2)", "question": "Differentiate f(x) = (4*x - 5)*sin(7*x**2 + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "14*x*(4*x - 5)*cos(7*x**2 + 2) + 4*sin(7*x**2 + 2)"} | |
| {"family": "product_trig_chain", "expression": "(7 - x)*sin(8*x**2 - 2)", "question": "Differentiate f(x) = (7 - x)*sin(8*x**2 - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "16*x*(7 - x)*cos(8*x**2 - 2) - sin(8*x**2 - 2)"} | |
| {"family": "trig_chain", "expression": "cos(3*x**2 - x + 6)", "question": "Differentiate f(x) = cos(3*x**2 - x + 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(6*x - 1)*sin(3*x**2 - x + 6)"} | |
| {"family": "trig_chain", "expression": "-sin(7*x**2 - 9*x + 3)", "question": "Differentiate f(x) = -sin(7*x**2 - 9*x + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(14*x - 9)*cos(7*x**2 - 9*x + 3)"} | |
| {"family": "product_trig_chain", "expression": "(8 - 7*x)*sin(5*x**2 + 3)", "question": "Differentiate f(x) = (8 - 7*x)*sin(5*x**2 + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x*(8 - 7*x)*cos(5*x**2 + 3) - 7*sin(5*x**2 + 3)"} | |
| {"family": "product", "expression": "(6 - 4*x**4)*(x + 4)", "question": "Differentiate f(x) = (6 - 4*x**4)*(x + 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-4*x**4 - 16*x**3*(x + 4) + 6"} | |
| {"family": "power_chain", "expression": "(4*x**2 + 4*x - 6)**2", "question": "Differentiate f(x) = (4*x**2 + 4*x - 6)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(16*x + 8)*(4*x**2 + 4*x - 6)"} | |
| {"family": "rational", "expression": "(-5*x - 1)/(6*x - 4)", "question": "Differentiate f(x) = (-5*x - 1)/(6*x - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-6*(-5*x - 1)/(6*x - 4)**2 - 5/(6*x - 4)"} | |
| {"family": "polynomial", "expression": "-4*x**3 + 13*x - 4", "question": "Differentiate f(x) = -4*x**3 + 13*x - 4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "13 - 12*x**2"} | |
| {"family": "polynomial", "expression": "4*x**5 + 7*x**3 - 9*x + 8", "question": "Differentiate f(x) = 4*x**5 + 7*x**3 - 9*x + 8 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "20*x**4 + 21*x**2 - 9"} | |
| {"family": "polynomial", "expression": "-8*x**4 + 2*x**2 + 8*x + 4", "question": "Differentiate f(x) = -8*x**4 + 2*x**2 + 8*x + 4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-32*x**3 + 4*x + 8"} | |
| {"family": "product", "expression": "(5*x + 5)*(-4*x**3 - 1)", "question": "Differentiate f(x) = (5*x + 5)*(-4*x**3 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-20*x**3 - 12*x**2*(5*x + 5) - 5"} | |
| {"family": "trig_chain", "expression": "-sin(2*x - 2)", "question": "Differentiate f(x) = -sin(2*x - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2*cos(2*x - 2)"} | |
| {"family": "product_trig_chain", "expression": "(-8*x - 2)*sin(2*x**2 - 7)", "question": "Differentiate f(x) = (-8*x - 2)*sin(2*x**2 - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*x*(-8*x - 2)*cos(2*x**2 - 7) - 8*sin(2*x**2 - 7)"} | |
| {"family": "product_trig_chain", "expression": "(-x - 8)*sin(6*x**2 - 1)", "question": "Differentiate f(x) = (-x - 8)*sin(6*x**2 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x*(-x - 8)*cos(6*x**2 - 1) - sin(6*x**2 - 1)"} | |
| {"family": "rational", "expression": "(7 - 8*x)/(x + 5)", "question": "Differentiate f(x) = (7 - 8*x)/(x + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(7 - 8*x)/(x + 5)**2 - 8/(x + 5)"} | |
| {"family": "rational", "expression": "(9 - 9*x)/(-5*x - 9)", "question": "Differentiate f(x) = (9 - 9*x)/(-5*x - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "5*(9 - 9*x)/(-5*x - 9)**2 - 9/(-5*x - 9)"} | |
| {"family": "polynomial", "expression": "5*x**3 - x - 9", "question": "Differentiate f(x) = 5*x**3 - x - 9 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "15*x**2 - 1"} | |
| {"family": "rational", "expression": "(1 - 3*x)/(9*x - 8)", "question": "Differentiate f(x) = (1 - 3*x)/(9*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*(1 - 3*x)/(9*x - 8)**2 - 3/(9*x - 8)"} | |
| {"family": "power_chain", "expression": "(-x**2 - 7*x - 4)**2", "question": "Differentiate f(x) = (-x**2 - 7*x - 4)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-4*x - 14)*(-x**2 - 7*x - 4)"} | |
| {"family": "power_chain", "expression": "(-4*x**2 - 7*x - 2)**5", "question": "Differentiate f(x) = (-4*x**2 - 7*x - 2)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-40*x - 35)*(-4*x**2 - 7*x - 2)**4"} | |
| {"family": "trig_chain", "expression": "cos(2*x**2 + 2*x - 3)", "question": "Differentiate f(x) = cos(2*x**2 + 2*x - 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(4*x + 2)*sin(2*x**2 + 2*x - 3)"} | |
| {"family": "product", "expression": "(2*x - 1)*(7*x**2 - 7)", "question": "Differentiate f(x) = (2*x - 1)*(7*x**2 - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "14*x**2 + 14*x*(2*x - 1) - 14"} | |
| {"family": "product_trig_chain", "expression": "(6 - 8*x)*(-sin(x**2 + 9))", "question": "Differentiate f(x) = (6 - 8*x)*(-sin(x**2 + 9)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2*x*(6 - 8*x)*cos(x**2 + 9) + 8*sin(x**2 + 9)"} | |
| {"family": "product_trig_chain", "expression": "(2*x + 6)*sin(2*x**2 + 8)", "question": "Differentiate f(x) = (2*x + 6)*sin(2*x**2 + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4*x*(2*x + 6)*cos(2*x**2 + 8) + 2*sin(2*x**2 + 8)"} | |
| {"family": "power_chain", "expression": "(-2*x**2 - 4*x + 9)**5", "question": "Differentiate f(x) = (-2*x**2 - 4*x + 9)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-20*x - 20)*(-2*x**2 - 4*x + 9)**4"} | |
| {"family": "trig_chain", "expression": "cos(5*x + 2)", "question": "Differentiate f(x) = cos(5*x + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-5*sin(5*x + 2)"} | |
| {"family": "product_trig_chain", "expression": "(x + 7)*(-sin(4*x**2 + 5))", "question": "Differentiate f(x) = (x + 7)*(-sin(4*x**2 + 5)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x*(x + 7)*cos(4*x**2 + 5) - sin(4*x**2 + 5)"} | |
| {"family": "product_trig_chain", "expression": "(-5*x - 1)*(-sin(9*x**2 - 4))", "question": "Differentiate f(x) = (-5*x - 1)*(-sin(9*x**2 - 4)) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-18*x*(-5*x - 1)*cos(9*x**2 - 4) + 5*sin(9*x**2 - 4)"} | |
| {"family": "trig_chain", "expression": "cos(7*x - 8)", "question": "Differentiate f(x) = cos(7*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-7*sin(7*x - 8)"} | |
| {"family": "trig_chain", "expression": "-sin(6*x**2 + 4*x + 7)", "question": "Differentiate f(x) = -sin(6*x**2 + 4*x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(12*x + 4)*cos(6*x**2 + 4*x + 7)"} | |
| {"family": "product", "expression": "(7*x + 1)*(5*x**2 + 4)", "question": "Differentiate f(x) = (7*x + 1)*(5*x**2 + 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "35*x**2 + 10*x*(7*x + 1) + 28"} | |
| {"family": "product_trig_chain", "expression": "(-x - 2)*sin(3*x**2 + 5)", "question": "Differentiate f(x) = (-x - 2)*sin(3*x**2 + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x*(-x - 2)*cos(3*x**2 + 5) - sin(3*x**2 + 5)"} | |
| {"family": "rational", "expression": "(7*x + 6)/(4*x + 1)", "question": "Differentiate f(x) = (7*x + 6)/(4*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "7/(4*x + 1) - 4*(7*x + 6)/(4*x + 1)**2"} | |
| {"family": "product", "expression": "(7 - 6*x)*(-x**3 - 1)", "question": "Differentiate f(x) = (7 - 6*x)*(-x**3 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x**3 - 3*x**2*(7 - 6*x) + 6"} | |
| {"family": "trig_chain", "expression": "sin(2*x - 5)", "question": "Differentiate f(x) = sin(2*x - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "2*cos(2*x - 5)"} | |
| {"family": "power_chain", "expression": "(-4*x**2 - 9*x - 9)**4", "question": "Differentiate f(x) = (-4*x**2 - 9*x - 9)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-32*x - 36)*(-4*x**2 - 9*x - 9)**3"} | |
| {"family": "rational", "expression": "(-7*x - 3)/(9 - 5*x)", "question": "Differentiate f(x) = (-7*x - 3)/(9 - 5*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-7/(9 - 5*x) + 5*(-7*x - 3)/(9 - 5*x)**2"} | |
| {"family": "rational", "expression": "(8*x + 8)/(-8*x - 9)", "question": "Differentiate f(x) = (8*x + 8)/(-8*x - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8/(-8*x - 9) + 8*(8*x + 8)/(-8*x - 9)**2"} | |