derivative of cos((x^3/(10)))

解

\frac{d}{d x} (cos (\frac{x ^{3}}{10}))

- \frac{3 x ^{2} sin ( \frac{x ^{3}}{10} )}{10}

解答ステップ

\frac{d}{d x} (cos (\frac{x ^{3}}{10}))

連鎖法則を適用:

- sin (\frac{x ^{3}}{10}) \frac{d}{d x} (\frac{x ^{3}}{10})

= - sin (\frac{x ^{3}}{10}) \frac{d}{d x} (\frac{x ^{3}}{10})

\frac{d}{d x} (\frac{x ^{3}}{10}) = \frac{3 x ^{2}}{10}

= - sin (\frac{x ^{3}}{10}) \frac{3 x ^{2}}{10}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 x ^{2} sin ( \frac{x ^{3}}{10} )}{10}