derivative of sqrt(9-x^8)

解

\frac{d}{d x} (9 - x^{8})

- \frac{4 x ^{7}}{9 - x ^{8}}

解答ステップ

\frac{d}{d x} (9 - x^{8})

連鎖法則を適用:

\frac{1}{2 9 - x ^{8}} \frac{d}{d x} (9 - x^{8})

= \frac{1}{2 9 - x ^{8}} \frac{d}{d x} (9 - x^{8})

\frac{d}{d x} (9 - x^{8}) = - 8 x^{7}

= \frac{1}{2 9 - x ^{8}} (- 8 x^{7})

簡素化

\frac{1}{2 9 - x ^{8}} (- 8 x^{7}) : - \frac{4 x ^{7}}{9 - x ^{8}}

= - \frac{4 x ^{7}}{9 - x ^{8}}