derivative of (1-x^{2/3})

解

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

- \frac{2}{3 ( 1 - x ) ^{\frac{1}{3}}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (1 - x) = - 1

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

簡素化

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