derivative of 1/((x+1^3(3x-1)^2))

解答

\frac{d}{d x} (\frac{1}{( x + 1 ) ^{3} ( 3 x - 1 ) ^{2}})

- \frac{3 ( 5 x + 1 )}{( x + 1 ) ^{4} ( 3 x - 1 ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{1}{( x + 1 ) ^{3} ( 3 x - 1 ) ^{2}})

使用指数法则:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} (((x + 1)^{3} (3 x - 1)^{2})^{- 1})

使用连锁律:

- \frac{1}{( ( x + 1 ) ^{3} ( 3 x - 1 ) ^{2} ) ^{2}} \frac{d}{d x} ((x + 1)^{3} (3 x - 1)^{2})

= - \frac{1}{( ( x + 1 ) ^{3} ( 3 x - 1 ) ^{2} ) ^{2}} \frac{d}{d x} ((x + 1)^{3} (3 x - 1)^{2})

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

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

化简

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

= - \frac{3 ( 5 x + 1 )}{( x + 1 ) ^{4} ( 3 x - 1 ) ^{3}}

\frac{d}{d x} ((\frac{x}{2})^{4})

d er i v a t i v e y (θ) = \frac{π}{7} cos (θ)

\int \frac{3 x + 1}{x ^{3} - x ^{2} + x - 1} d x

\int e^{x} sin (y) d x

\frac{d}{d x} (y^{2} - 2 y \cdot cos (x))