derivative 2\sqrt[5]{x^3}

解答

导数

\frac{6 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}}

求解步骤

将常数提出:

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

使用连锁律:

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

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

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

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

化简

2 \cdot \frac{1}{5 ( x ^{3} ) ^{\frac{4}{5}}} \cdot 3 x^{2} : \frac{6 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}}

= \frac{6 x ^{2}}{5 ( x ^{3} ) ^{\frac{4}{5}}}