derivative \sqrt[5]{x^4}

解

導関数

5 x^{4}

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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