derivative sin^3(cos(8x))

解

導関数

sin^{3} (cos (8 x))

- 24 sin^{2} (cos (8 x)) cos (cos (8 x)) sin (8 x)

解答ステップ

\frac{d}{d x} (sin^{3} (cos (8 x)))

連鎖法則を適用:

3 (sin (cos (8 x)))^{2} \frac{d}{d x} (sin (cos (8 x)))

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

\frac{d}{d x} (sin (cos (8 x))) = - 8 cos (cos (8 x)) sin (8 x)

= 3 (sin (cos (8 x)))^{2} (- 8 cos (cos (8 x)) sin (8 x))

簡素化

= - 24 sin^{2} (cos (8 x)) cos (cos (8 x)) sin (8 x)