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

解

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

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

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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