derivative 1/(\sqrt[3]{(9x+1)^2)}

解答

导数

\frac{1}{3 ( 9 x + 1 ) ^{2}}

- \frac{6 ( 9 x + 1 )}{( ( 9 x + 1 ) ^{2} ) ^{\frac{4}{3}}}

求解步骤

\frac{d}{d x} \frac{1}{3 ( 9 x + 1 ) ^{2}}

使用指数法则:

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

= \frac{d}{d x} (((9 x + 1)^{2})^{- \frac{1}{3}})

使用连锁律:

- \frac{1}{3 ( ( 9 x + 1 ) ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} ((9 x + 1)^{2})

= - \frac{1}{3 ( ( 9 x + 1 ) ^{2} ) ^{\frac{4}{3}}} \frac{d}{d x} ((9 x + 1)^{2})

\frac{d}{d x} ((9 x + 1)^{2}) = 18 (9 x + 1)

= - \frac{1}{3 ( ( 9 x + 1 ) ^{2} ) ^{\frac{4}{3}}} \cdot 18 (9 x + 1)

化简

- \frac{1}{3 ( ( 9 x + 1 ) ^{2} ) ^{\frac{4}{3}}} \cdot 18 (9 x + 1) : - \frac{6 ( 9 x + 1 )}{( ( 9 x + 1 ) ^{2} ) ^{\frac{4}{3}}}

= - \frac{6 ( 9 x + 1 )}{( ( 9 x + 1 ) ^{2} ) ^{\frac{4}{3}}}

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