derivative of (3/x ^{14})

解

\frac{d}{d x} ((\frac{3}{x})^{14})

- \frac{66961566}{x ^{15}}

解答ステップ

\frac{d}{d x} ((\frac{3}{x})^{14})

連鎖法則を適用:

14 (\frac{3}{x})^{13} \frac{d}{d x} (\frac{3}{x})

= 14 (\frac{3}{x})^{13} \frac{d}{d x} (\frac{3}{x})

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

= 14 (\frac{3}{x})^{13} (- \frac{3}{x ^{2}})

簡素化

14 (\frac{3}{x})^{13} (- \frac{3}{x ^{2}}) : - \frac{66961566}{x ^{15}}

= - \frac{66961566}{x ^{15}}