derivative f(x)=(3+x^5)^{2/3}

解答

导数

f (x) = (3 + x^{5})^{\frac{2}{3}}

\frac{10 x ^{4}}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}}

求解步骤

\frac{d}{d x} ((3 + x^{5})^{\frac{2}{3}})

使用连锁律:

\frac{2}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}} \frac{d}{d x} (3 + x^{5})

= \frac{2}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}} \frac{d}{d x} (3 + x^{5})

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

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

化简

\frac{2}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}} \cdot 5 x^{4} : \frac{10 x ^{4}}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}}

= \frac{10 x ^{4}}{3 ( 3 + x ^{5} ) ^{\frac{1}{3}}}

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