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

解

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

2 x sin (x)

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

簡素化

2 cos (x) - 2 (cos (x) - x sin (x)) : 2 x sin (x)

= 2 x sin (x)