derivative ((3t-2)^3)/(t+5)

解答

导数

\frac{( 3 t - 2 ) ^{3}}{t + 5}

\frac{9 ( 3 t - 2 ) ^{2} ( t + 5 ) - ( 3 t - 2 ) ^{3}}{( t + 5 ) ^{2}}

求解步骤

\frac{d}{d t} (\frac{( 3 t - 2 ) ^{3}}{t + 5})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( ( 3 t - 2 ) ^{3} ) ( t + 5 ) - \frac{d}{d t} ( t + 5 ) ( 3 t - 2 ) ^{3}}{( t + 5 ) ^{2}}

\frac{d}{d t} ((3 t - 2)^{3}) = 9 (3 t - 2)^{2}

\frac{d}{d t} (t + 5) = 1

= \frac{9 ( 3 t - 2 ) ^{2} ( t + 5 ) - 1 \cdot ( 3 t - 2 ) ^{3}}{( t + 5 ) ^{2}}

化简

= \frac{9 ( 3 t - 2 ) ^{2} ( t + 5 ) - ( 3 t - 2 ) ^{3}}{( t + 5 ) ^{2}}

\frac{\partial}{\partial x} ((e^{x} - 4 x) sin (y))

t an g e n t y = (x - 2) (x^{2} + 4), (1, - 5)

d er i v a t i v e ln (2)

\frac{d y}{d x} = \frac{y}{x + 1} + 4 x^{2} + 4 x

\int_{\frac{4}{3}}^{4} \frac{1}{1 - x ^{2}} d x