derivative of sqrt((2-x^3))

解

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

- \frac{3 - x + 2}{2}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{3 - x + 2}{2}