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

解

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

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

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

和/差の法則を適用:

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

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

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

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

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