derivative of cos^4(sin^3(x))

解

\frac{d}{d x} (cos^{4} (sin^{3} (x)))

- 12 cos^{3} (sin^{3} (x)) sin^{2} (x) sin (sin^{3} (x)) cos (x)

解答ステップ

\frac{d}{d x} (cos^{4} (sin^{3} (x)))

連鎖法則を適用:

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

= 4 (cos (sin^{3} (x)))^{3} \frac{d}{d x} (cos (sin^{3} (x)))

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

= 4 (cos (sin^{3} (x)))^{3} (- sin (sin^{3} (x)) \cdot 3 sin^{2} (x) cos (x))

簡素化

= - 12 cos^{3} (sin^{3} (x)) sin^{2} (x) sin (sin^{3} (x)) cos (x)