derivative of (2/(x^3)^2)

解

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

- \frac{24}{x ^{7}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{2}{x ^{3}}) = - \frac{6}{x ^{4}}

= 2 \cdot \frac{2}{x ^{3}} (- \frac{6}{x ^{4}})

簡素化

2 \cdot \frac{2}{x ^{3}} (- \frac{6}{x ^{4}}) : - \frac{24}{x ^{7}}

= - \frac{24}{x ^{7}}