derivative sin^8(cos(2x))

解

導関数

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

- 16 sin^{7} (cos (2 x)) cos (cos (2 x)) sin (2 x)

解答ステップ

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

連鎖法則を適用:

8 (sin (cos (2 x)))^{7} \frac{d}{d x} (sin (cos (2 x)))

= 8 (sin (cos (2 x)))^{7} \frac{d}{d x} (sin (cos (2 x)))

\frac{d}{d x} (sin (cos (2 x))) = - 2 cos (cos (2 x)) sin (2 x)

= 8 (sin (cos (2 x)))^{7} (- 2 cos (cos (2 x)) sin (2 x))

簡素化

= - 16 sin^{7} (cos (2 x)) cos (cos (2 x)) sin (2 x)