| {"family": "polynomial", "expression": "8 - 3*x**3", "question": "Differentiate f(x) = 8 - 3*x**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*x**2"} | |
| {"family": "product", "expression": "(2 - 3*x)*(3 - 2*x**2)", "question": "Differentiate f(x) = (2 - 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": "6*x**2 - 4*x*(2 - 3*x) - 9"} | |
| {"family": "trig_chain", "expression": "sin(6*x**2 + 3*x + 7)", "question": "Differentiate f(x) = sin(6*x**2 + 3*x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(12*x + 3)*cos(6*x**2 + 3*x + 7)"} | |
| {"family": "product", "expression": "(2*x - 4)*(9*x**4 - 8)", "question": "Differentiate f(x) = (2*x - 4)*(9*x**4 - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "18*x**4 + 36*x**3*(2*x - 4) - 16"} | |
| {"family": "power_chain", "expression": "(-6*x**2 + 5*x - 3)**4", "question": "Differentiate f(x) = (-6*x**2 + 5*x - 3)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(20 - 48*x)*(-6*x**2 + 5*x - 3)**3"} | |
| {"family": "trig_chain", "expression": "sin(8*x**2 + x + 7)", "question": "Differentiate f(x) = sin(8*x**2 + x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(16*x + 1)*cos(8*x**2 + x + 7)"} | |
| {"family": "product", "expression": "(3*x - 9)*(9*x**3 - 2)", "question": "Differentiate f(x) = (3*x - 9)*(9*x**3 - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "27*x**3 + 27*x**2*(3*x - 9) - 6"} | |
| {"family": "polynomial", "expression": "8*x**5 + 7*x**3 + 8*x + 9", "question": "Differentiate f(x) = 8*x**5 + 7*x**3 + 8*x + 9 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "40*x**4 + 21*x**2 + 8"} | |
| {"family": "trig_chain", "expression": "sin(9*x**2 - 9*x + 6)", "question": "Differentiate f(x) = sin(9*x**2 - 9*x + 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(18*x - 9)*cos(9*x**2 - 9*x + 6)"} | |
| {"family": "power_chain", "expression": "(2*x**2 + 9*x + 8)**5", "question": "Differentiate f(x) = (2*x**2 + 9*x + 8)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(20*x + 45)*(2*x**2 + 9*x + 8)**4"} | |
| {"family": "product", "expression": "(5*x - 7)*(2*x**2 + 4)", "question": "Differentiate f(x) = (5*x - 7)*(2*x**2 + 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x**2 + 4*x*(5*x - 7) + 20"} | |
| {"family": "product", "expression": "(8*x - 8)*(-5*x**2 - 5)", "question": "Differentiate f(x) = (8*x - 8)*(-5*x**2 - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-40*x**2 - 10*x*(8*x - 8) - 40"} | |
| {"family": "power_chain", "expression": "(-x**2 + 7*x - 9)**2", "question": "Differentiate f(x) = (-x**2 + 7*x - 9)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(14 - 4*x)*(-x**2 + 7*x - 9)"} | |
| {"family": "power_chain", "expression": "(-x**2 - 3*x + 1)**5", "question": "Differentiate f(x) = (-x**2 - 3*x + 1)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-10*x - 15)*(-x**2 - 3*x + 1)**4"} | |
| {"family": "trig_chain", "expression": "-sin(2*x - 6)", "question": "Differentiate f(x) = -sin(2*x - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2*cos(2*x - 6)"} | |
| {"family": "product", "expression": "(-2*x - 3)*(-8*x**4 - 5)", "question": "Differentiate f(x) = (-2*x - 3)*(-8*x**4 - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "16*x**4 - 32*x**3*(-2*x - 3) + 10"} | |
| {"family": "power_chain", "expression": "(-6*x**2 + 4*x + 7)**2", "question": "Differentiate f(x) = (-6*x**2 + 4*x + 7)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(8 - 24*x)*(-6*x**2 + 4*x + 7)"} | |
| {"family": "power_chain", "expression": "(4*x**2 - 7*x + 8)**2", "question": "Differentiate f(x) = (4*x**2 - 7*x + 8)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(16*x - 14)*(4*x**2 - 7*x + 8)"} | |
| {"family": "polynomial", "expression": "-2*x**6 + 9*x**4 - 5*x + 3", "question": "Differentiate f(x) = -2*x**6 + 9*x**4 - 5*x + 3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x**5 + 36*x**3 - 5"} | |
| {"family": "trig_chain", "expression": "sin(-4*x**2 + 4*x + 5)", "question": "Differentiate f(x) = sin(-4*x**2 + 4*x + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(4 - 8*x)*cos(-4*x**2 + 4*x + 5)"} | |
| {"family": "polynomial", "expression": "-8*x**4 + 9*x**2 + 7*x - 9", "question": "Differentiate f(x) = -8*x**4 + 9*x**2 + 7*x - 9 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-32*x**3 + 18*x + 7"} | |
| {"family": "trig_chain", "expression": "-sin(8*x**2 + 3*x + 5)", "question": "Differentiate f(x) = -sin(8*x**2 + 3*x + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(16*x + 3)*cos(8*x**2 + 3*x + 5)"} | |
| {"family": "rational", "expression": "(2*x + 1)/(2*x + 8)", "question": "Differentiate f(x) = (2*x + 1)/(2*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-2*(2*x + 1)/(2*x + 8)**2 + 2/(2*x + 8)"} | |
| {"family": "power_chain", "expression": "(6*x**2 - 2*x + 6)**3", "question": "Differentiate f(x) = (6*x**2 - 2*x + 6)**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 + 6)**2"} | |
| {"family": "power_chain", "expression": "(-x**2 - 3*x + 3)**5", "question": "Differentiate f(x) = (-x**2 - 3*x + 3)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-10*x - 15)*(-x**2 - 3*x + 3)**4"} | |
| {"family": "polynomial", "expression": "-x**3 - 2*x - 4", "question": "Differentiate f(x) = -x**3 - 2*x - 4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-3*x**2 - 2"} | |
| {"family": "rational", "expression": "(5*x + 1)/(6 - x)", "question": "Differentiate f(x) = (5*x + 1)/(6 - x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "5/(6 - x) + (5*x + 1)/(6 - x)**2"} | |
| {"family": "product", "expression": "(1 - 2*x)*(-7*x**2 - 6)", "question": "Differentiate f(x) = (1 - 2*x)*(-7*x**2 - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "14*x**2 - 14*x*(1 - 2*x) + 12"} | |
| {"family": "rational", "expression": "(2 - x)/(7*x - 9)", "question": "Differentiate f(x) = (2 - x)/(7*x - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-7*(2 - x)/(7*x - 9)**2 - 1/(7*x - 9)"} | |
| {"family": "rational", "expression": "(3*x - 5)/(-7*x - 6)", "question": "Differentiate f(x) = (3*x - 5)/(-7*x - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "3/(-7*x - 6) + 7*(3*x - 5)/(-7*x - 6)**2"} | |
| {"family": "rational", "expression": "(9*x + 8)/(1 - 4*x)", "question": "Differentiate f(x) = (9*x + 8)/(1 - 4*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9/(1 - 4*x) + 4*(9*x + 8)/(1 - 4*x)**2"} | |
| {"family": "polynomial", "expression": "-9*x**5 - x**3 - 8*x - 3", "question": "Differentiate f(x) = -9*x**5 - x**3 - 8*x - 3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-45*x**4 - 3*x**2 - 8"} | |
| {"family": "polynomial", "expression": "-8*x**6 + 2*x**4 - 4*x - 6", "question": "Differentiate f(x) = -8*x**6 + 2*x**4 - 4*x - 6 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-48*x**5 + 8*x**3 - 4"} | |
| {"family": "power_chain", "expression": "(-3*x**2 + 7*x - 7)**2", "question": "Differentiate f(x) = (-3*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 - 12*x)*(-3*x**2 + 7*x - 7)"} | |
| {"family": "rational", "expression": "(9 - x)/(x - 2)", "question": "Differentiate f(x) = (9 - x)/(x - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(9 - x)/(x - 2)**2 - 1/(x - 2)"} | |
| {"family": "polynomial", "expression": "-3*x**3 + x + 1", "question": "Differentiate f(x) = -3*x**3 + x + 1 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "1 - 9*x**2"} | |
| {"family": "power_chain", "expression": "(-7*x**2 + 2*x - 8)**4", "question": "Differentiate f(x) = (-7*x**2 + 2*x - 8)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(8 - 56*x)*(-7*x**2 + 2*x - 8)**3"} | |
| {"family": "polynomial", "expression": "-7*x**4 + 6*x**2 + 5*x - 8", "question": "Differentiate f(x) = -7*x**4 + 6*x**2 + 5*x - 8 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-28*x**3 + 12*x + 5"} | |
| {"family": "polynomial", "expression": "-7*x**4 + 2*x**2 + 2*x - 6", "question": "Differentiate f(x) = -7*x**4 + 2*x**2 + 2*x - 6 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-28*x**3 + 4*x + 2"} | |
| {"family": "power_chain", "expression": "(-3*x**2 - 7*x - 6)**2", "question": "Differentiate f(x) = (-3*x**2 - 7*x - 6)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-12*x - 14)*(-3*x**2 - 7*x - 6)"} | |
| {"family": "rational", "expression": "(x + 3)/(-5*x - 8)", "question": "Differentiate f(x) = (x + 3)/(-5*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "1/(-5*x - 8) + 5*(x + 3)/(-5*x - 8)**2"} | |
| {"family": "product", "expression": "(4 - 4*x**4)*(2*x + 2)", "question": "Differentiate f(x) = (4 - 4*x**4)*(2*x + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x**4 - 16*x**3*(2*x + 2) + 8"} | |
| {"family": "trig_chain", "expression": "cos(3*x**2 + 3*x - 4)", "question": "Differentiate f(x) = cos(3*x**2 + 3*x - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(6*x + 3)*sin(3*x**2 + 3*x - 4)"} | |
| {"family": "product", "expression": "(5*x - 3)*(6*x**3 + 2)", "question": "Differentiate f(x) = (5*x - 3)*(6*x**3 + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "30*x**3 + 18*x**2*(5*x - 3) + 10"} | |
| {"family": "power_chain", "expression": "(-9*x**2 + 8*x + 9)**3", "question": "Differentiate f(x) = (-9*x**2 + 8*x + 9)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(24 - 54*x)*(-9*x**2 + 8*x + 9)**2"} | |
| {"family": "product", "expression": "(7 - 3*x)*(4*x**2 + 2)", "question": "Differentiate f(x) = (7 - 3*x)*(4*x**2 + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x**2 + 8*x*(7 - 3*x) - 6"} | |
| {"family": "product", "expression": "(3*x + 3)*(x**2 - 4)", "question": "Differentiate f(x) = (3*x + 3)*(x**2 - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "3*x**2 + 2*x*(3*x + 3) - 12"} | |
| {"family": "rational", "expression": "(-9*x - 2)/(9*x - 7)", "question": "Differentiate f(x) = (-9*x - 2)/(9*x - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*(-9*x - 2)/(9*x - 7)**2 - 9/(9*x - 7)"} | |
| {"family": "power_chain", "expression": "(2*x**2 - 5*x - 8)**4", "question": "Differentiate f(x) = (2*x**2 - 5*x - 8)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(16*x - 20)*(2*x**2 - 5*x - 8)**3"} | |
| {"family": "polynomial", "expression": "6*x**5 + 3*x**3 - 3*x - 2", "question": "Differentiate f(x) = 6*x**5 + 3*x**3 - 3*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 - 3"} | |
| {"family": "power_chain", "expression": "(-4*x**2 + 4*x - 8)**5", "question": "Differentiate f(x) = (-4*x**2 + 4*x - 8)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(20 - 40*x)*(-4*x**2 + 4*x - 8)**4"} | |
| {"family": "power_chain", "expression": "(4*x**2 - 7*x + 4)**5", "question": "Differentiate f(x) = (4*x**2 - 7*x + 4)**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 + 4)**4"} | |
| {"family": "product", "expression": "(9*x + 9)*(6*x**4 + 3)", "question": "Differentiate f(x) = (9*x + 9)*(6*x**4 + 3) 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 + 9) + 27"} | |
| {"family": "product", "expression": "(6*x - 3)*(8*x**2 + 7)", "question": "Differentiate f(x) = (6*x - 3)*(8*x**2 + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "48*x**2 + 16*x*(6*x - 3) + 42"} | |
| {"family": "polynomial", "expression": "9*x**3 + 3*x + 5", "question": "Differentiate f(x) = 9*x**3 + 3*x + 5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "27*x**2 + 3"} | |
| {"family": "trig_chain", "expression": "-sin(2*x**2 + 9*x - 3)", "question": "Differentiate f(x) = -sin(2*x**2 + 9*x - 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(4*x + 9)*cos(2*x**2 + 9*x - 3)"} | |
| {"family": "trig_chain", "expression": "sin(-4*x**2 + 5*x + 8)", "question": "Differentiate f(x) = sin(-4*x**2 + 5*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(5 - 8*x)*cos(-4*x**2 + 5*x + 8)"} | |
| {"family": "power_chain", "expression": "(-7*x**2 + 2*x - 4)**4", "question": "Differentiate f(x) = (-7*x**2 + 2*x - 4)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(8 - 56*x)*(-7*x**2 + 2*x - 4)**3"} | |
| {"family": "rational", "expression": "(7*x - 5)/(-5*x - 2)", "question": "Differentiate f(x) = (7*x - 5)/(-5*x - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "7/(-5*x - 2) + 5*(7*x - 5)/(-5*x - 2)**2"} | |
| {"family": "power_chain", "expression": "(-8*x**2 - 4*x + 4)**5", "question": "Differentiate f(x) = (-8*x**2 - 4*x + 4)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-80*x - 20)*(-8*x**2 - 4*x + 4)**4"} | |
| {"family": "trig_chain", "expression": "-sin(8*x + 5)", "question": "Differentiate f(x) = -sin(8*x + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*cos(8*x + 5)"} | |
| {"family": "polynomial", "expression": "-2*x**3 + 15*x + 1", "question": "Differentiate f(x) = -2*x**3 + 15*x + 1 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "15 - 6*x**2"} | |
| {"family": "polynomial", "expression": "5*x**4 - x**2 + 9*x + 1", "question": "Differentiate f(x) = 5*x**4 - x**2 + 9*x + 1 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "20*x**3 - 2*x + 9"} | |
| {"family": "product", "expression": "(4 - 8*x)*(x**3 + 2)", "question": "Differentiate f(x) = (4 - 8*x)*(x**3 + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x**3 + 3*x**2*(4 - 8*x) - 16"} | |
| {"family": "power_chain", "expression": "(3*x**2 + 4*x - 1)**4", "question": "Differentiate f(x) = (3*x**2 + 4*x - 1)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(24*x + 16)*(3*x**2 + 4*x - 1)**3"} | |
| {"family": "polynomial", "expression": "5*x**3 + 13*x + 3", "question": "Differentiate f(x) = 5*x**3 + 13*x + 3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "15*x**2 + 13"} | |
| {"family": "rational", "expression": "(8 - 8*x)/(9*x + 3)", "question": "Differentiate f(x) = (8 - 8*x)/(9*x + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*(8 - 8*x)/(9*x + 3)**2 - 8/(9*x + 3)"} | |
| {"family": "trig_chain", "expression": "-sin(x - 2)", "question": "Differentiate f(x) = -sin(x - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-cos(x - 2)"} | |
| {"family": "product", "expression": "(6 - x**4)*(3*x - 5)", "question": "Differentiate f(x) = (6 - x**4)*(3*x - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-3*x**4 - 4*x**3*(3*x - 5) + 18"} | |
| {"family": "rational", "expression": "(4 - 5*x)/(8 - 9*x)", "question": "Differentiate f(x) = (4 - 5*x)/(8 - 9*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9*(4 - 5*x)/(8 - 9*x)**2 - 5/(8 - 9*x)"} | |
| {"family": "trig_chain", "expression": "-sin(-x**2 + 9*x + 7)", "question": "Differentiate f(x) = -sin(-x**2 + 9*x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(9 - 2*x)*cos(-x**2 + 9*x + 7)"} | |
| {"family": "polynomial", "expression": "-5*x**6 - 2*x**4 + 9*x - 8", "question": "Differentiate f(x) = -5*x**6 - 2*x**4 + 9*x - 8 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-30*x**5 - 8*x**3 + 9"} | |
| {"family": "trig_chain", "expression": "sin(-4*x**2 + 2*x + 6)", "question": "Differentiate f(x) = sin(-4*x**2 + 2*x + 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(2 - 8*x)*cos(-4*x**2 + 2*x + 6)"} | |
| {"family": "polynomial", "expression": "8*x**6 - 3*x**4 - 6*x + 5", "question": "Differentiate f(x) = 8*x**6 - 3*x**4 - 6*x + 5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "48*x**5 - 12*x**3 - 6"} | |
| {"family": "trig_chain", "expression": "sin(-2*x**2 + 6*x + 7)", "question": "Differentiate f(x) = sin(-2*x**2 + 6*x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(6 - 4*x)*cos(-2*x**2 + 6*x + 7)"} | |
| {"family": "power_chain", "expression": "(4*x**2 + 2*x - 2)**2", "question": "Differentiate f(x) = (4*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": "(16*x + 4)*(4*x**2 + 2*x - 2)"} | |
| {"family": "rational", "expression": "(x + 6)/(-8*x - 2)", "question": "Differentiate f(x) = (x + 6)/(-8*x - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "1/(-8*x - 2) + 8*(x + 6)/(-8*x - 2)**2"} | |
| {"family": "rational", "expression": "(2 - 6*x)/(7*x + 6)", "question": "Differentiate f(x) = (2 - 6*x)/(7*x + 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-7*(2 - 6*x)/(7*x + 6)**2 - 6/(7*x + 6)"} | |
| {"family": "polynomial", "expression": "-3*x**6 + 3*x**4 - x + 9", "question": "Differentiate f(x) = -3*x**6 + 3*x**4 - 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 - 1"} | |
| {"family": "polynomial", "expression": "-3*x**4 - x**2 + 2*x + 1", "question": "Differentiate f(x) = -3*x**4 - x**2 + 2*x + 1 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x**3 - 2*x + 2"} | |
| {"family": "polynomial", "expression": "4*x**5 - 2*x**3 + 4*x - 6", "question": "Differentiate f(x) = 4*x**5 - 2*x**3 + 4*x - 6 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "20*x**4 - 6*x**2 + 4"} | |
| {"family": "product", "expression": "(2 - 8*x**3)*(-2*x - 5)", "question": "Differentiate f(x) = (2 - 8*x**3)*(-2*x - 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "16*x**3 - 24*x**2*(-2*x - 5) - 4"} | |
| {"family": "product", "expression": "(-4*x - 5)*(-7*x**4 - 9)", "question": "Differentiate f(x) = (-4*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": "28*x**4 - 28*x**3*(-4*x - 5) + 36"} | |
| {"family": "polynomial", "expression": "2*x**6 + 3*x**4 + 6*x + 5", "question": "Differentiate f(x) = 2*x**6 + 3*x**4 + 6*x + 5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x**5 + 12*x**3 + 6"} | |
| {"family": "product", "expression": "(2 - 3*x)*(6*x**2 + 9)", "question": "Differentiate f(x) = (2 - 3*x)*(6*x**2 + 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-18*x**2 + 12*x*(2 - 3*x) - 27"} | |
| {"family": "power_chain", "expression": "(8*x**2 + 6*x + 5)**2", "question": "Differentiate f(x) = (8*x**2 + 6*x + 5)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(32*x + 12)*(8*x**2 + 6*x + 5)"} | |
| {"family": "polynomial", "expression": "8*x**5 - 2*x**3 - 8*x - 6", "question": "Differentiate f(x) = 8*x**5 - 2*x**3 - 8*x - 6 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "40*x**4 - 6*x**2 - 8"} | |
| {"family": "product", "expression": "(-x - 6)*(5*x**4 + 5)", "question": "Differentiate f(x) = (-x - 6)*(5*x**4 + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-5*x**4 + 20*x**3*(-x - 6) - 5"} | |
| {"family": "trig_chain", "expression": "cos(8*x**2 - 5*x + 7)", "question": "Differentiate f(x) = cos(8*x**2 - 5*x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(16*x - 5)*sin(8*x**2 - 5*x + 7)"} | |
| {"family": "rational", "expression": "(8*x + 5)/(-7*x - 8)", "question": "Differentiate f(x) = (8*x + 5)/(-7*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8/(-7*x - 8) + 7*(8*x + 5)/(-7*x - 8)**2"} | |
| {"family": "rational", "expression": "(3*x + 6)/(7*x + 8)", "question": "Differentiate f(x) = (3*x + 6)/(7*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-7*(3*x + 6)/(7*x + 8)**2 + 3/(7*x + 8)"} | |
| {"family": "rational", "expression": "(4 - 6*x)/(9*x - 8)", "question": "Differentiate f(x) = (4 - 6*x)/(9*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*(4 - 6*x)/(9*x - 8)**2 - 6/(9*x - 8)"} | |
| {"family": "rational", "expression": "(3 - 7*x)/(5*x - 4)", "question": "Differentiate f(x) = (3 - 7*x)/(5*x - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-5*(3 - 7*x)/(5*x - 4)**2 - 7/(5*x - 4)"} | |
| {"family": "trig_chain", "expression": "sin(x**2 + 5*x - 9)", "question": "Differentiate f(x) = sin(x**2 + 5*x - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(2*x + 5)*cos(x**2 + 5*x - 9)"} | |
| {"family": "rational", "expression": "(8 - 4*x)/(-x - 4)", "question": "Differentiate f(x) = (8 - 4*x)/(-x - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(8 - 4*x)/(-x - 4)**2 - 4/(-x - 4)"} | |
| {"family": "polynomial", "expression": "9*x**4 + 9*x**2 - 7*x - 9", "question": "Differentiate f(x) = 9*x**4 + 9*x**2 - 7*x - 9 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "36*x**3 + 18*x - 7"} | |
| {"family": "product", "expression": "(-6*x - 9)*(6*x**2 + 3)", "question": "Differentiate f(x) = (-6*x - 9)*(6*x**2 + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-36*x**2 + 12*x*(-6*x - 9) - 18"} | |
| {"family": "trig_chain", "expression": "sin(2*x**2 - 5*x + 8)", "question": "Differentiate f(x) = sin(2*x**2 - 5*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(4*x - 5)*cos(2*x**2 - 5*x + 8)"} | |
| {"family": "product", "expression": "(9*x - 4)*(9*x**4 + 1)", "question": "Differentiate f(x) = (9*x - 4)*(9*x**4 + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "81*x**4 + 36*x**3*(9*x - 4) + 9"} | |
| {"family": "polynomial", "expression": "-6*x**4 + 9*x**2 + 9*x - 5", "question": "Differentiate f(x) = -6*x**4 + 9*x**2 + 9*x - 5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-24*x**3 + 18*x + 9"} | |
| {"family": "product", "expression": "(9 - 9*x**3)*(x - 8)", "question": "Differentiate f(x) = (9 - 9*x**3)*(x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*x**3 - 27*x**2*(x - 8) + 9"} | |
| {"family": "trig_chain", "expression": "-sin(-2*x**2 + 4*x + 6)", "question": "Differentiate f(x) = -sin(-2*x**2 + 4*x + 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(4 - 4*x)*cos(-2*x**2 + 4*x + 6)"} | |
| {"family": "trig_chain", "expression": "sin(-5*x**2 + 6*x + 7)", "question": "Differentiate f(x) = sin(-5*x**2 + 6*x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(6 - 10*x)*cos(-5*x**2 + 6*x + 7)"} | |
| {"family": "polynomial", "expression": "-8*x**3 + 6*x - 8", "question": "Differentiate f(x) = -8*x**3 + 6*x - 8 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6 - 24*x**2"} | |
| {"family": "rational", "expression": "(1 - 2*x)/(-6*x - 4)", "question": "Differentiate f(x) = (1 - 2*x)/(-6*x - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*(1 - 2*x)/(-6*x - 4)**2 - 2/(-6*x - 4)"} | |
| {"family": "trig_chain", "expression": "sin(9*x - 6)", "question": "Differentiate f(x) = sin(9*x - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9*cos(9*x - 6)"} | |
| {"family": "product", "expression": "(5 - 9*x**3)*(4*x - 8)", "question": "Differentiate f(x) = (5 - 9*x**3)*(4*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-36*x**3 - 27*x**2*(4*x - 8) + 20"} | |
| {"family": "product", "expression": "(5*x + 4)*(9*x**3 + 2)", "question": "Differentiate f(x) = (5*x + 4)*(9*x**3 + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "45*x**3 + 27*x**2*(5*x + 4) + 10"} | |
| {"family": "trig_chain", "expression": "sin(3*x**2 + 9*x - 1)", "question": "Differentiate f(x) = sin(3*x**2 + 9*x - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(6*x + 9)*cos(3*x**2 + 9*x - 1)"} | |
| {"family": "trig_chain", "expression": "cos(-6*x**2 + x + 2)", "question": "Differentiate f(x) = cos(-6*x**2 + x + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(1 - 12*x)*sin(-6*x**2 + x + 2)"} | |
| {"family": "rational", "expression": "(-x - 2)/(9 - 6*x)", "question": "Differentiate f(x) = (-x - 2)/(9 - 6*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-1/(9 - 6*x) + 6*(-x - 2)/(9 - 6*x)**2"} | |
| {"family": "trig_chain", "expression": "cos(4*x**2 + x + 6)", "question": "Differentiate f(x) = cos(4*x**2 + x + 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(8*x + 1)*sin(4*x**2 + x + 6)"} | |
| {"family": "polynomial", "expression": "-3*x**4 + 8*x**2 + 5*x + 6", "question": "Differentiate f(x) = -3*x**4 + 8*x**2 + 5*x + 6 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x**3 + 16*x + 5"} | |
| {"family": "polynomial", "expression": "-4*x**5 + 8*x**3 - 6*x + 8", "question": "Differentiate f(x) = -4*x**5 + 8*x**3 - 6*x + 8 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-20*x**4 + 24*x**2 - 6"} | |
| {"family": "product", "expression": "(x + 6)*(6*x**3 - 9)", "question": "Differentiate f(x) = (x + 6)*(6*x**3 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x**3 + 18*x**2*(x + 6) - 9"} | |
| {"family": "polynomial", "expression": "-5*x**3 - 10*x - 9", "question": "Differentiate f(x) = -5*x**3 - 10*x - 9 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-15*x**2 - 10"} | |
| {"family": "product", "expression": "(x + 7)*(9*x**2 - 8)", "question": "Differentiate f(x) = (x + 7)*(9*x**2 - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9*x**2 + 18*x*(x + 7) - 8"} | |
| {"family": "trig_chain", "expression": "-sin(9*x**2 - 6*x + 6)", "question": "Differentiate f(x) = -sin(9*x**2 - 6*x + 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(18*x - 6)*cos(9*x**2 - 6*x + 6)"} | |
| {"family": "polynomial", "expression": "-2*x**4 - 3*x**2 + 2*x - 2", "question": "Differentiate f(x) = -2*x**4 - 3*x**2 + 2*x - 2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*x**3 - 6*x + 2"} | |
| {"family": "trig_chain", "expression": "cos(8*x**2 + 4*x - 9)", "question": "Differentiate f(x) = cos(8*x**2 + 4*x - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(16*x + 4)*sin(8*x**2 + 4*x - 9)"} | |
| {"family": "power_chain", "expression": "(-9*x**2 + 3*x - 7)**5", "question": "Differentiate f(x) = (-9*x**2 + 3*x - 7)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(15 - 90*x)*(-9*x**2 + 3*x - 7)**4"} | |
| {"family": "power_chain", "expression": "(6*x**2 + 6*x - 7)**3", "question": "Differentiate f(x) = (6*x**2 + 6*x - 7)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(36*x + 18)*(6*x**2 + 6*x - 7)**2"} | |
| {"family": "trig_chain", "expression": "cos(9*x**2 + 6*x + 1)", "question": "Differentiate f(x) = cos(9*x**2 + 6*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(18*x + 6)*sin(9*x**2 + 6*x + 1)"} | |
| {"family": "rational", "expression": "(2 - 2*x)/(-6*x - 9)", "question": "Differentiate f(x) = (2 - 2*x)/(-6*x - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*(2 - 2*x)/(-6*x - 9)**2 - 2/(-6*x - 9)"} | |
| {"family": "rational", "expression": "(-3*x - 3)/(6*x + 8)", "question": "Differentiate f(x) = (-3*x - 3)/(6*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-6*(-3*x - 3)/(6*x + 8)**2 - 3/(6*x + 8)"} | |
| {"family": "product", "expression": "(4*x + 1)*(9*x**4 - 1)", "question": "Differentiate f(x) = (4*x + 1)*(9*x**4 - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "36*x**4 + 36*x**3*(4*x + 1) - 4"} | |
| {"family": "power_chain", "expression": "(8*x**2 + x - 4)**3", "question": "Differentiate f(x) = (8*x**2 + x - 4)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(48*x + 3)*(8*x**2 + x - 4)**2"} | |
| {"family": "product", "expression": "(8*x - 8)*(4*x**2 + 2)", "question": "Differentiate f(x) = (8*x - 8)*(4*x**2 + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "32*x**2 + 8*x*(8*x - 8) + 16"} | |
| {"family": "trig_chain", "expression": "sin(2*x**2 + 7*x - 8)", "question": "Differentiate f(x) = sin(2*x**2 + 7*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(4*x + 7)*cos(2*x**2 + 7*x - 8)"} | |
| {"family": "rational", "expression": "(2 - 4*x)/(8 - x)", "question": "Differentiate f(x) = (2 - 4*x)/(8 - x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(2 - 4*x)/(8 - x)**2 - 4/(8 - x)"} | |
| {"family": "product", "expression": "(-8*x - 1)*(-x**2 - 9)", "question": "Differentiate f(x) = (-8*x - 1)*(-x**2 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "8*x**2 - 2*x*(-8*x - 1) + 72"} | |
| {"family": "rational", "expression": "(9*x - 6)/(8*x - 2)", "question": "Differentiate f(x) = (9*x - 6)/(8*x - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9/(8*x - 2) - 8*(9*x - 6)/(8*x - 2)**2"} | |
| {"family": "polynomial", "expression": "9*x**6 - 4*x**4 - x - 1", "question": "Differentiate f(x) = 9*x**6 - 4*x**4 - x - 1 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "54*x**5 - 16*x**3 - 1"} | |
| {"family": "power_chain", "expression": "(4*x**2 + 2*x - 6)**5", "question": "Differentiate f(x) = (4*x**2 + 2*x - 6)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(40*x + 10)*(4*x**2 + 2*x - 6)**4"} | |
| {"family": "power_chain", "expression": "(9*x**2 + 2*x - 4)**3", "question": "Differentiate f(x) = (9*x**2 + 2*x - 4)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(54*x + 6)*(9*x**2 + 2*x - 4)**2"} | |
| {"family": "trig_chain", "expression": "cos(5*x**2 + 4*x + 9)", "question": "Differentiate f(x) = cos(5*x**2 + 4*x + 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(10*x + 4)*sin(5*x**2 + 4*x + 9)"} | |
| {"family": "rational", "expression": "(-8*x - 5)/(5*x + 8)", "question": "Differentiate f(x) = (-8*x - 5)/(5*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-5*(-8*x - 5)/(5*x + 8)**2 - 8/(5*x + 8)"} | |
| {"family": "trig_chain", "expression": "cos(2*x**2 - 4*x + 2)", "question": "Differentiate f(x) = cos(2*x**2 - 4*x + 2) 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 + 2)"} | |
| {"family": "trig_chain", "expression": "sin(2*x**2 - 3*x + 1)", "question": "Differentiate f(x) = sin(2*x**2 - 3*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(4*x - 3)*cos(2*x**2 - 3*x + 1)"} | |
| {"family": "trig_chain", "expression": "-sin(-7*x**2 + x + 8)", "question": "Differentiate f(x) = -sin(-7*x**2 + x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(1 - 14*x)*cos(-7*x**2 + x + 8)"} | |
| {"family": "rational", "expression": "(4*x - 3)/(8*x - 6)", "question": "Differentiate f(x) = (4*x - 3)/(8*x - 6) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-8*(4*x - 3)/(8*x - 6)**2 + 4/(8*x - 6)"} | |
| {"family": "rational", "expression": "(9*x - 3)/(9 - 8*x)", "question": "Differentiate f(x) = (9*x - 3)/(9 - 8*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9/(9 - 8*x) + 8*(9*x - 3)/(9 - 8*x)**2"} | |
| {"family": "polynomial", "expression": "-6*x**5 + 9*x**3 - 7*x + 9", "question": "Differentiate f(x) = -6*x**5 + 9*x**3 - 7*x + 9 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-30*x**4 + 27*x**2 - 7"} | |
| {"family": "power_chain", "expression": "(-6*x**2 + 8*x + 7)**2", "question": "Differentiate f(x) = (-6*x**2 + 8*x + 7)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(16 - 24*x)*(-6*x**2 + 8*x + 7)"} | |
| {"family": "polynomial", "expression": "4*x**3 - 2*x - 7", "question": "Differentiate f(x) = 4*x**3 - 2*x - 7 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "12*x**2 - 2"} | |
| {"family": "rational", "expression": "(7 - x)/(3*x - 2)", "question": "Differentiate f(x) = (7 - x)/(3*x - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-3*(7 - x)/(3*x - 2)**2 - 1/(3*x - 2)"} | |
| {"family": "trig_chain", "expression": "cos(-7*x**2 + 9*x + 8)", "question": "Differentiate f(x) = cos(-7*x**2 + 9*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(9 - 14*x)*sin(-7*x**2 + 9*x + 8)"} | |
| {"family": "rational", "expression": "(7*x + 6)/(3 - 8*x)", "question": "Differentiate f(x) = (7*x + 6)/(3 - 8*x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "7/(3 - 8*x) + 8*(7*x + 6)/(3 - 8*x)**2"} | |
| {"family": "trig_chain", "expression": "cos(-5*x**2 + 6*x + 8)", "question": "Differentiate f(x) = cos(-5*x**2 + 6*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(6 - 10*x)*sin(-5*x**2 + 6*x + 8)"} | |
| {"family": "product", "expression": "(2*x + 9)*(3*x**4 - 9)", "question": "Differentiate f(x) = (2*x + 9)*(3*x**4 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x**4 + 12*x**3*(2*x + 9) - 18"} | |
| {"family": "product", "expression": "(1 - 5*x)*(6 - 9*x**4)", "question": "Differentiate f(x) = (1 - 5*x)*(6 - 9*x**4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "45*x**4 - 36*x**3*(1 - 5*x) - 30"} | |
| {"family": "power_chain", "expression": "(-x**2 + 2*x + 7)**3", "question": "Differentiate f(x) = (-x**2 + 2*x + 7)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(6 - 6*x)*(-x**2 + 2*x + 7)**2"} | |
| {"family": "product", "expression": "(3*x + 8)*(2*x**3 - 2)", "question": "Differentiate f(x) = (3*x + 8)*(2*x**3 - 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "6*x**3 + 6*x**2*(3*x + 8) - 6"} | |
| {"family": "product", "expression": "(9 - 3*x)*(-8*x**4 - 4)", "question": "Differentiate f(x) = (9 - 3*x)*(-8*x**4 - 4) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "24*x**4 - 32*x**3*(9 - 3*x) + 12"} | |
| {"family": "trig_chain", "expression": "cos(8*x**2 + 9*x + 7)", "question": "Differentiate f(x) = cos(8*x**2 + 9*x + 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(16*x + 9)*sin(8*x**2 + 9*x + 7)"} | |
| {"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": "(6*x - 7)*(6*x**4 + 2)", "question": "Differentiate f(x) = (6*x - 7)*(6*x**4 + 2) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "36*x**4 + 24*x**3*(6*x - 7) + 12"} | |
| {"family": "power_chain", "expression": "(2*x**2 + 8*x - 5)**2", "question": "Differentiate f(x) = (2*x**2 + 8*x - 5)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(8*x + 16)*(2*x**2 + 8*x - 5)"} | |
| {"family": "power_chain", "expression": "(-9*x**2 - 6*x - 6)**5", "question": "Differentiate f(x) = (-9*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": "(-90*x - 30)*(-9*x**2 - 6*x - 6)**4"} | |
| {"family": "polynomial", "expression": "-5*x**4 + 3*x**2 - 6*x - 1", "question": "Differentiate f(x) = -5*x**4 + 3*x**2 - 6*x - 1 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-20*x**3 + 6*x - 6"} | |
| {"family": "rational", "expression": "(3*x - 6)/(4*x - 1)", "question": "Differentiate f(x) = (3*x - 6)/(4*x - 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-4*(3*x - 6)/(4*x - 1)**2 + 3/(4*x - 1)"} | |
| {"family": "product", "expression": "(9 - 9*x)*(8*x**2 - 9)", "question": "Differentiate f(x) = (9 - 9*x)*(8*x**2 - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-72*x**2 + 16*x*(9 - 9*x) + 81"} | |
| {"family": "polynomial", "expression": "-8*x**5 - 7*x**3 - 5*x + 5", "question": "Differentiate f(x) = -8*x**5 - 7*x**3 - 5*x + 5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-40*x**4 - 21*x**2 - 5"} | |
| {"family": "rational", "expression": "(1 - 9*x)/(-2*x - 9)", "question": "Differentiate f(x) = (1 - 9*x)/(-2*x - 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "2*(1 - 9*x)/(-2*x - 9)**2 - 9/(-2*x - 9)"} | |
| {"family": "power_chain", "expression": "(8*x**2 + 7*x - 8)**4", "question": "Differentiate f(x) = (8*x**2 + 7*x - 8)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(64*x + 28)*(8*x**2 + 7*x - 8)**3"} | |
| {"family": "rational", "expression": "(-3*x - 2)/(3 - x)", "question": "Differentiate f(x) = (-3*x - 2)/(3 - x) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-3/(3 - x) + (-3*x - 2)/(3 - x)**2"} | |
| {"family": "product", "expression": "(6*x - 6)*(-2*x**3 - 7)", "question": "Differentiate f(x) = (6*x - 6)*(-2*x**3 - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-12*x**3 - 6*x**2*(6*x - 6) - 42"} | |
| {"family": "product", "expression": "(7*x + 3)*(2*x**4 + 3)", "question": "Differentiate f(x) = (7*x + 3)*(2*x**4 + 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "14*x**4 + 8*x**3*(7*x + 3) + 21"} | |
| {"family": "power_chain", "expression": "(-6*x**2 + 4*x - 1)**4", "question": "Differentiate f(x) = (-6*x**2 + 4*x - 1)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(16 - 48*x)*(-6*x**2 + 4*x - 1)**3"} | |
| {"family": "polynomial", "expression": "-8*x**6 - 4*x**4 + 5*x - 4", "question": "Differentiate f(x) = -8*x**6 - 4*x**4 + 5*x - 4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-48*x**5 - 16*x**3 + 5"} | |
| {"family": "rational", "expression": "(9*x - 9)/(4*x + 8)", "question": "Differentiate f(x) = (9*x - 9)/(4*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9/(4*x + 8) - 4*(9*x - 9)/(4*x + 8)**2"} | |
| {"family": "rational", "expression": "(4*x - 9)/(-9*x - 8)", "question": "Differentiate f(x) = (4*x - 9)/(-9*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4/(-9*x - 8) + 9*(4*x - 9)/(-9*x - 8)**2"} | |
| {"family": "trig_chain", "expression": "sin(-5*x**2 + 5*x + 1)", "question": "Differentiate f(x) = sin(-5*x**2 + 5*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(5 - 10*x)*cos(-5*x**2 + 5*x + 1)"} | |
| {"family": "polynomial", "expression": "-3*x**5 - 5*x**3 - x - 7", "question": "Differentiate f(x) = -3*x**5 - 5*x**3 - x - 7 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-15*x**4 - 15*x**2 - 1"} | |
| {"family": "product", "expression": "(2*x + 8)*(x**2 - 1)", "question": "Differentiate f(x) = (2*x + 8)*(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 + 2*x*(2*x + 8) - 2"} | |
| {"family": "trig_chain", "expression": "cos(-4*x**2 + x + 5)", "question": "Differentiate f(x) = cos(-4*x**2 + x + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(1 - 8*x)*sin(-4*x**2 + x + 5)"} | |
| {"family": "power_chain", "expression": "(3*x**2 - 8*x - 2)**2", "question": "Differentiate f(x) = (3*x**2 - 8*x - 2)**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 - 2)"} | |
| {"family": "power_chain", "expression": "(-8*x**2 + 6*x + 9)**3", "question": "Differentiate f(x) = (-8*x**2 + 6*x + 9)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(18 - 48*x)*(-8*x**2 + 6*x + 9)**2"} | |
| {"family": "rational", "expression": "(-9*x - 8)/(-9*x - 3)", "question": "Differentiate f(x) = (-9*x - 8)/(-9*x - 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9*(-9*x - 8)/(-9*x - 3)**2 - 9/(-9*x - 3)"} | |
| {"family": "power_chain", "expression": "(8*x**2 + 8*x - 4)**3", "question": "Differentiate f(x) = (8*x**2 + 8*x - 4)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(48*x + 24)*(8*x**2 + 8*x - 4)**2"} | |
| {"family": "power_chain", "expression": "(-6*x**2 - 7*x - 8)**5", "question": "Differentiate f(x) = (-6*x**2 - 7*x - 8)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-60*x - 35)*(-6*x**2 - 7*x - 8)**4"} | |
| {"family": "power_chain", "expression": "(-4*x**2 + x - 1)**3", "question": "Differentiate f(x) = (-4*x**2 + x - 1)**3 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(3 - 24*x)*(-4*x**2 + x - 1)**2"} | |
| {"family": "product", "expression": "(6 - 7*x**3)*(-2*x - 7)", "question": "Differentiate f(x) = (6 - 7*x**3)*(-2*x - 7) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "14*x**3 - 21*x**2*(-2*x - 7) - 12"} | |
| {"family": "polynomial", "expression": "-4*x**4 - 5*x**2 - 2*x - 7", "question": "Differentiate f(x) = -4*x**4 - 5*x**2 - 2*x - 7 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-16*x**3 - 10*x - 2"} | |
| {"family": "trig_chain", "expression": "cos(x**2 + 3*x - 8)", "question": "Differentiate f(x) = cos(x**2 + 3*x - 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-(2*x + 3)*sin(x**2 + 3*x - 8)"} | |
| {"family": "power_chain", "expression": "(-9*x**2 + 3*x + 8)**4", "question": "Differentiate f(x) = (-9*x**2 + 3*x + 8)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(12 - 72*x)*(-9*x**2 + 3*x + 8)**3"} | |
| {"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": "rational", "expression": "(7*x + 2)/(2*x + 8)", "question": "Differentiate f(x) = (7*x + 2)/(2*x + 8) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "7/(2*x + 8) - 2*(7*x + 2)/(2*x + 8)**2"} | |
| {"family": "power_chain", "expression": "(-6*x**2 + 6*x + 7)**4", "question": "Differentiate f(x) = (-6*x**2 + 6*x + 7)**4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(24 - 48*x)*(-6*x**2 + 6*x + 7)**3"} | |
| {"family": "polynomial", "expression": "-7*x**4 + x**2 + 4*x + 9", "question": "Differentiate f(x) = -7*x**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": "-28*x**3 + 2*x + 4"} | |
| {"family": "polynomial", "expression": "9*x**6 - 4*x**4 + 2*x + 4", "question": "Differentiate f(x) = 9*x**6 - 4*x**4 + 2*x + 4 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "54*x**5 - 16*x**3 + 2"} | |
| {"family": "power_chain", "expression": "(-4*x**2 + 3*x - 8)**2", "question": "Differentiate f(x) = (-4*x**2 + 3*x - 8)**2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(6 - 16*x)*(-4*x**2 + 3*x - 8)"} | |
| {"family": "power_chain", "expression": "(-7*x**2 - 2*x + 3)**5", "question": "Differentiate f(x) = (-7*x**2 - 2*x + 3)**5 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "(-70*x - 10)*(-7*x**2 - 2*x + 3)**4"} | |
| {"family": "product", "expression": "(-8*x - 9)*(3*x**4 + 9)", "question": "Differentiate f(x) = (-8*x - 9)*(3*x**4 + 9) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-24*x**4 + 12*x**3*(-8*x - 9) - 72"} | |
| {"family": "rational", "expression": "(3 - x)/(9*x + 5)", "question": "Differentiate f(x) = (3 - x)/(9*x + 5) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-9*(3 - x)/(9*x + 5)**2 - 1/(9*x + 5)"} | |
| {"family": "rational", "expression": "(4*x + 7)/(4*x - 3)", "question": "Differentiate f(x) = (4*x + 7)/(4*x - 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "4/(4*x - 3) - 4*(4*x + 7)/(4*x - 3)**2"} | |
| {"family": "rational", "expression": "(4*x - 5)/(6*x + 1)", "question": "Differentiate f(x) = (4*x - 5)/(6*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-6*(4*x - 5)/(6*x + 1)**2 + 4/(6*x + 1)"} | |
| {"family": "rational", "expression": "(9*x - 3)/(-x - 3)", "question": "Differentiate f(x) = (9*x - 3)/(-x - 3) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "9/(-x - 3) + (9*x - 3)/(-x - 3)**2"} | |
| {"family": "polynomial", "expression": "2*x**5 - 6*x**3 + 5*x - 2", "question": "Differentiate f(x) = 2*x**5 - 6*x**3 + 5*x - 2 with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "10*x**4 - 18*x**2 + 5"} | |
| {"family": "trig_chain", "expression": "-sin(3*x + 1)", "question": "Differentiate f(x) = -sin(3*x + 1) with respect to x. Return one line: Final answer: <SymPy expression using x, +, -, *, /, **, sin, cos>. Do not explain.", "answer": "-3*cos(3*x + 1)"} | |