derivative f(x)= 6/(\sqrt[9]{x^7+5)}

解答

导数

f (x) = \frac{6}{9 x ^{7} + 5}

- \frac{14 x ^{6}}{3 ( x ^{7} + 5 ) ^{\frac{10}{9}}}

求解步骤

\frac{d}{d x} (\frac{6}{9 x ^{7} + 5})

将常数提出:

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

= 6 \frac{d}{d x} (\frac{1}{9 x ^{7} + 5})

使用指数法则:

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

= 6 \frac{d}{d x} ((x^{7} + 5)^{- \frac{1}{9}})

使用连锁律:

- \frac{1}{9 ( x ^{7} + 5 ) ^{\frac{10}{9}}} \frac{d}{d x} (x^{7} + 5)

= - \frac{1}{9 ( x ^{7} + 5 ) ^{\frac{10}{9}}} \frac{d}{d x} (x^{7} + 5)

\frac{d}{d x} (x^{7} + 5) = 7 x^{6}

= 6 (- \frac{1}{9 ( x ^{7} + 5 ) ^{\frac{10}{9}}} \cdot 7 x^{6})

化简

6 (- \frac{1}{9 ( x ^{7} + 5 ) ^{\frac{10}{9}}} \cdot 7 x^{6}) : - \frac{14 x ^{6}}{3 ( x ^{7} + 5 ) ^{\frac{10}{9}}}

= - \frac{14 x ^{6}}{3 ( x ^{7} + 5 ) ^{\frac{10}{9}}}

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