derivative of 2sin^3(x-3cos^2(x))

解

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

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

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (2 sin^{3} (x)) = 6 sin^{2} (x) cos (x)

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

= 6 sin^{2} (x) cos (x) - (- 3 sin (2 x))

簡素化

= 6 sin^{2} (x) cos (x) + 3 sin (2 x)