derivative of cos(sin^3(5x-5))

解

\frac{d}{d x} (cos (sin^{3} (5 x - 5)))

- sin (sin^{3} (5 x - 5)) \cdot 15 sin^{2} (5 x - 5) cos (5 x - 5)

解答ステップ

\frac{d}{d x} (cos (sin^{3} (5 x - 5)))

連鎖法則を適用:

- sin (sin^{3} (5 x - 5)) \frac{d}{d x} (sin^{3} (5 x - 5))

= - sin (sin^{3} (5 x - 5)) \frac{d}{d x} (sin^{3} (5 x - 5))

\frac{d}{d x} (sin^{3} (5 x - 5)) = 15 sin^{2} (5 x - 5) cos (5 x - 5)

= - sin (sin^{3} (5 x - 5)) \cdot 15 sin^{2} (5 x - 5) cos (5 x - 5)