derivative of ((-2x-3^7)/((4x+2)^4))

解答

\frac{d}{d x} (\frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}})

- \frac{( - 2 x - 3 ) ^{6} ( 6 x - 5 )}{8 ( 2 x + 1 ) ^{5}}

求解步骤

\frac{d}{d x} (\frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}})

使用微分除法定则:

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

= \frac{\frac{d}{d x} ( ( - 2 x - 3 ) ^{7} ) ( 4 x + 2 ) ^{4} - \frac{d}{d x} ( ( 4 x + 2 ) ^{4} ) ( - 2 x - 3 ) ^{7}}{( ( 4 x + 2 ) ^{4} ) ^{2}}

\frac{d}{d x} ((- 2 x - 3)^{7}) = - 14 (- 2 x - 3)^{6}

\frac{d}{d x} ((4 x + 2)^{4}) = 16 (4 x + 2)^{3}

= \frac{( - 14 ( - 2 x - 3 ) ^{6} ) ( 4 x + 2 ) ^{4} - 16 ( 4 x + 2 ) ^{3} ( - 2 x - 3 ) ^{7}}{( ( 4 x + 2 ) ^{4} ) ^{2}}

化简

\frac{( - 14 ( - 2 x - 3 ) ^{6} ) ( 4 x + 2 ) ^{4} - 16 ( 4 x + 2 ) ^{3} ( - 2 x - 3 ) ^{7}}{( ( 4 x + 2 ) ^{4} ) ^{2}} : - \frac{( - 2 x - 3 ) ^{6} ( 6 x - 5 )}{8 ( 2 x + 1 ) ^{5}}

= - \frac{( - 2 x - 3 ) ^{6} ( 6 x - 5 )}{8 ( 2 x + 1 ) ^{5}}

\frac{d y}{d x} + 10 y = 8

\int_{1}^{5} x^{3} - 5 x^{2} - x + 5 d x

\frac{d}{d y} (2 1 - y^{2} - (\frac{x}{4})^{2})

d er i v a t i v e f (x) = 17.19 8^{2} - x^{2}

\frac{d}{d x} (e^{x e^{y}})