derivative of 20cos(2x-30sin(2x))

解

\frac{d}{d x} (20 cos (2 x) - 30 sin (2 x))

- 40 sin (2 x) - 60 cos (2 x)

解答ステップ

\frac{d}{d x} (20 cos (2 x) - 30 sin (2 x))

和/差の法則を適用:

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

= \frac{d}{d x} (20 cos (2 x)) - \frac{d}{d x} (30 sin (2 x))

\frac{d}{d x} (20 cos (2 x)) = - 40 sin (2 x)

\frac{d}{d x} (30 sin (2 x)) = 60 cos (2 x)

= - 40 sin (2 x) - 60 cos (2 x)