derivative 8/((8-x^4)^{3/2)}

解答

导数

\frac{8}{( 8 - x ^{4} ) ^{\frac{3}{2}}}

\frac{48 x ^{3}}{( 8 - x ^{4} ) ^{\frac{5}{2}}}

求解步骤

\frac{d}{d x} (\frac{8}{( 8 - x ^{4} ) ^{\frac{3}{2}}})

将常数提出:

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

= 8 \frac{d}{d x} (\frac{1}{( 8 - x ^{4} ) ^{\frac{3}{2}}})

使用指数法则:

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

= 8 \frac{d}{d x} ((8 - x^{4})^{- \frac{3}{2}})

使用连锁律:

- \frac{3}{2 ( 8 - x ^{4} ) ^{\frac{5}{2}}} \frac{d}{d x} (8 - x^{4})

= - \frac{3}{2 ( 8 - x ^{4} ) ^{\frac{5}{2}}} \frac{d}{d x} (8 - x^{4})

\frac{d}{d x} (8 - x^{4}) = - 4 x^{3}

= 8 (- \frac{3}{2 ( 8 - x ^{4} ) ^{\frac{5}{2}}} (- 4 x^{3}))

化简

8 (- \frac{3}{2 ( 8 - x ^{4} ) ^{\frac{5}{2}}} (- 4 x^{3})) : \frac{48 x ^{3}}{( 8 - x ^{4} ) ^{\frac{5}{2}}}

= \frac{48 x ^{3}}{( 8 - x ^{4} ) ^{\frac{5}{2}}}

\frac{d}{d x} (33 arctan (x))

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

\frac{\partial}{\partial y} (8)

\frac{d}{d x} (ln (\frac{9 x}{x ^{2} + 15}))

\frac{d}{d x} (\frac{cos ( x )}{x ^{7}})