derivative of-5cos(cos(x^6))

解

\frac{d}{d x} (- 5 cos (cos (x^{6})))

- 30 x^{5} sin (cos (x^{6})) sin (x^{6})

解答ステップ

\frac{d}{d x} (- 5 cos (cos (x^{6})))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - 5 \frac{d}{d x} (cos (cos (x^{6})))

連鎖法則を適用:

- sin (cos (x^{6})) \frac{d}{d x} (cos (x^{6}))

= - sin (cos (x^{6})) \frac{d}{d x} (cos (x^{6}))

\frac{d}{d x} (cos (x^{6})) = - sin (x^{6}) \cdot 6 x^{5}

= - 5 (- sin (cos (x^{6})) (- sin (x^{6}) \cdot 6 x^{5}))

簡素化

= - 30 x^{5} sin (cos (x^{6})) sin (x^{6})