derivative f(x)=sqrt(8-x^3)

解

導関数

f (x) = 8 - x^{3}

- \frac{3 x ^{2}}{2 8 - x ^{3}}

解答ステップ

\frac{d}{d x} (8 - x^{3})

連鎖法則を適用:

\frac{1}{2 8 - x ^{3}} \frac{d}{d x} (8 - x^{3})

= \frac{1}{2 8 - x ^{3}} \frac{d}{d x} (8 - x^{3})

\frac{d}{d x} (8 - x^{3}) = - 3 x^{2}

= \frac{1}{2 8 - x ^{3}} (- 3 x^{2})

簡素化

\frac{1}{2 8 - x ^{3}} (- 3 x^{2}) : - \frac{3 x ^{2}}{2 8 - x ^{3}}

= - \frac{3 x ^{2}}{2 8 - x ^{3}}