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7 + b = 0 \implies b = -7 |
\frac{d}{dy}\left(\cos{\left(y\right)}\right) = -\sin{\left(y\right)} |
\frac{d}{db}\left(0\right) = 0 |
\frac{d}{dx}\left(x^3 \sin{\left(x\right)}\right) = 3 x^2 \sin{\left(x\right)} + x^3 \cos{\left(x\right)} |
\log_{5}\left(4 + 3 w\right) = 2 \implies w = 7 |
46 - 23 = 23 |
8 a + a^2 = 0 \implies a \in \{ -8, 0 \} |
(1, -2, 3) \times (3, -1, 3) = (-3, 6, 5) |
-18 \cdot 41 = -738 |
\lim_{t \to -1} \left(5 - t\right) = 6 |
-3 + w = 0 \implies w = 3 |
\lim_{w \to 0} \left(\sin{\left(w\right)}\right) = 0 |
\frac{d}{dw}\left(\cos{\left(w\right)}\right) = -\sin{\left(w\right)} |
(1, -5, 0) \times (5, -3, 4) = (-20, -4, 22) |
\int \left(1\right) du = u + C |
\frac{d}{du}\left(\cos{\left(u\right)} \left(4 + u\right)\right) = -\sin{\left(u\right)} \left(4 + u\right) + \cos{\left(u\right)} |
\int \left(-\sin{\left(v\right)}\right) dv = -1 + \cos{\left(v\right)} + C |
\frac{d}{db}\left(9 b^3\right) = 27 b^2 |
-8 - 7 c + c^2 = 0 \implies c \in \{ -1, 8 \} |
\int \left(2 u\right) du = u^2 + C |
-14 - 5 x + x^2 = 0 \implies x \in \{ -2, 7 \} |
\cos{\left(x\right)} \left(-3 - x\right) = -x \cos{\left(x\right)} - 3 \cos{\left(x\right)} |
\int \left(1\right) da = a + C |
\int \left(-2 w\right) dw = -w^2 + C |
f(w) = 5 + 3 w + w^2, \quad g(y) = 4 + 3 y \implies f(g(y)) = 33 + 33 y + 9 y^2 |
\frac{d}{dv}\left(-3 v^3\right) = -9 v^2 |
\log_{3}\left(8 + 4 u\right) = 3 \implies u = \frac{19}{4} |
-32 - 4 y + y^2 = 0 \implies y \in \{ -4, 8 \} |
22 + 40 = 62 |
-294 - 49 u + 6 u^2 + u^3 = 0 \implies u \in \{ -7, -6, 7 \} |
\lim_{t \to -5} \left(t\right) = -5 |
(3, 4, 5) \times (2, 5, 2) = (-17, 4, 7) |
(-4, 1, 3) \times (0, -2, 4) = (10, 16, 8) |
f(t) = 3 + 3 t + t^2, \quad g(x) = 1 + 3 x \implies f(g(x)) = 7 + 15 x + 9 x^2 |
\log_{5}\left(5 + z\right) = 3 \implies z = 120 |
30 - 2 = 28 |
16 + 10 a + a^2 = 0 \implies a \in \{ -8, -2 \} |
\log_{3}\left(4 + 4 t\right) = 1 \implies t = \frac{-1}{4} |
\lim_{t \to -4} \left(0\right) = 0 |
18 - 28 = -10 |
\log_{2}\left(6 + t\right) = 2 \implies t = -2 |
-21 - 4 c + c^2 = 0 \implies c \in \{ -3, 7 \} |
(-2, 4, -5) \times (2, 1, -2) = (-3, -14, -10) |
\int \left(1 - 3 z^2\right) dz = z - z^3 + C |
(5, -5, -5) \times (-3, 5, 1) = (20, 10, 10) |
\frac{d}{db}\left(b^5\right) = 5 b^4 |
f(b) = 3 + 5 b + b^2, \quad g(c) = 2 + c \implies f(g(c)) = 17 + 9 c + c^2 |
(1, -2, 2) \times (2, -1, 4) = (-6, 0, 3) |
\lim_{b \to -5} \left(4 b\right) = -20 |
\frac{d}{dt}\left(-4 t + t^2\right) = -4 + 2 t |
(-5, 4, 1) \times (5, -5, 2) = (13, 15, 5) |
-\left(-8 + x\right) = 8 - x |
\log_{4}\left(3 + 2 v\right) = 1 \implies v = \frac{1}{2} |
\frac{d}{dw}\left(w \sin{\left(w\right)}\right) = w \cos{\left(w\right)} + \sin{\left(w\right)} |
\frac{17}{45} = \frac{17}{45} |
2 u \left(5 - u\right) = 10 u - 2 u^2 |
-4 - 28 = -32 |
f(x) = 2 + 2 x + x^2, \quad g(b) = 3 + 3 b \implies f(g(b)) = 17 + 24 b + 9 b^2 |
\int \left(1\right) db = b + C |
\frac{-37}{47} = \frac{-37}{47} |
(4, -1, -3) \times (-5, -2, 4) = (-10, -1, -13) |
(-5, -3, -3) \times (2, 0, -5) = (15, -31, 6) |
f(z) = 2 + 3 z + z^2, \quad g(y) = 1 + 3 y \implies f(g(y)) = 6 + 15 y + 9 y^2 |
\frac{34}{36} = \frac{17}{18} |
f(v) = 1 + 2 v + v^2, \quad g(c) = 1 + 2 c \implies f(g(c)) = 4 + 8 c + 4 c^2 |
\log_{5}\left(7 + 4 u\right) = 2 \implies u = \frac{9}{2} |
f(u) = 5 + 2 u + u^2, \quad g(y) = 2 + y \implies f(g(y)) = 13 + 6 y + y^2 |
56 + 6 c - 9 c^2 + c^3 = 0 \implies c \in \{ -2, 4, 7 \} |
\int \left(2\right) dz = 2 z + C |
\frac{d}{du}\left(u\right) = 1 |
-3 - 39 = -42 |
7 + 44 = 51 |
\int \left(1 + 2 z\right) dz = z + z^2 + C |
(5, -4, 5) \times (-1, 3, -3) = (-3, 10, 11) |
\lim_{w \to 1} \left(w^2\right) = 1 |
-6 + x + x^2 = 0 \implies x \in \{ -3, 2 \} |
-15 - 2 a + a^2 = 0 \implies a \in \{ -3, 5 \} |
\int \left(7 v^6\right) dv = v^7 + C |
9 \cdot 7 = 63 |
\log_{3}\left(6 + 3 c\right) = 2 \implies c = 1 |
-5 + 4 w + w^2 = 0 \implies w \in \{ -5, 1 \} |
-24 + 5 t + t^2 = 0 \implies t \in \{ -8, 3 \} |
\log_{3}\left(5 + w\right) = 2 \implies w = 4 |
\int \left(3 u^2\right) du = u^3 + C |
(4, -5, -3) \times (1, 0, -2) = (10, 5, 5) |
f(u) = 3 + 4 u + u^2, \quad g(x) = 4 + x \implies f(g(x)) = 35 + 12 x + x^2 |
w^2 \left(8 + t\right) = t w^2 + 8 w^2 |
-9 + a^2 = 0 \implies a \in \{ -3, 3 \} |
\log_{3}\left(8 + 3 b\right) = 3 \implies b = \frac{19}{3} |
5 + t = 0 \implies t = -5 |
\frac{d}{dz}\left(\sin{\left(z\right)}\right) = \cos{\left(z\right)} |
-24 w - 5 w^2 + w^3 = 0 \implies w \in \{ -3, 0, 8 \} |
30 - 50 = -20 |
f(t) = 1 + 4 t + t^2, \quad g(w) = 3 + 3 w \implies f(g(w)) = 22 + 30 w + 9 w^2 |
\frac{d}{db}\left(\cos{\left(b\right)}\right) = -\sin{\left(b\right)} |
-3 + u = 0 \implies u = 3 |
2 y + y^2 = 0 \implies y \in \{ -2, 0 \} |
f(u) = 5 + 5 u + u^2, \quad g(w) = 4 + 2 w \implies f(g(w)) = 41 + 26 w + 4 w^2 |
\int \left(-\sin{\left(c\right)}\right) dc = -1 + \cos{\left(c\right)} + C |
\log_{4}\left(7 + 4 u\right) = 2 \implies u = \frac{9}{4} |
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