derivative 3/((1-x^2)^4)

解答

导数

\frac{3}{( 1 - x ^{2} ) ^{4}}

\frac{24 x}{( 1 - x ^{2} ) ^{5}}

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (\frac{1}{( 1 - x ^{2} ) ^{4}})

使用指数法则:

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

= 3 \frac{d}{d x} ((1 - x^{2})^{- 4})

使用连锁律:

- \frac{4}{( 1 - x ^{2} ) ^{5}} \frac{d}{d x} (1 - x^{2})

= - \frac{4}{( 1 - x ^{2} ) ^{5}} \frac{d}{d x} (1 - x^{2})

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

= 3 (- \frac{4}{( 1 - x ^{2} ) ^{5}} (- 2 x))

化简

3 (- \frac{4}{( 1 - x ^{2} ) ^{5}} (- 2 x)) : \frac{24 x}{( 1 - x ^{2} ) ^{5}}

= \frac{24 x}{( 1 - x ^{2} ) ^{5}}

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

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\frac{\partial}{\partial x} (x^{y^{x}})

\int \frac{1}{x ^{2} + 64} d x

t an g e n t y = 2 x^{3} - x^{2} + 2