derivative \sqrt[5]{1/(y^2)}

解

導関数

5 \frac{1}{y ^{2}}

- \frac{2 ( y ^{2} ) ^{\frac{4}{5}}}{5 y ^{3}}

解答ステップ

\frac{d}{d y} (5 \frac{1}{y ^{2}})

連鎖法則を適用:

\frac{1}{5 ( \frac{1}{y ^{2}} ) ^{\frac{4}{5}}} \frac{d}{d y} (\frac{1}{y ^{2}})

= \frac{1}{5 ( \frac{1}{y ^{2}} ) ^{\frac{4}{5}}} \frac{d}{d y} (\frac{1}{y ^{2}})

\frac{d}{d y} (\frac{1}{y ^{2}}) = - \frac{2}{y ^{3}}

= \frac{1}{5 ( \frac{1}{y ^{2}} ) ^{\frac{4}{5}}} (- \frac{2}{y ^{3}})

簡素化

\frac{1}{5 ( \frac{1}{y ^{2}} ) ^{\frac{4}{5}}} (- \frac{2}{y ^{3}}) : - \frac{2 ( y ^{2} ) ^{\frac{4}{5}}}{5 y ^{3}}

= - \frac{2 ( y ^{2} ) ^{\frac{4}{5}}}{5 y ^{3}}