derivative of-2cos(xsin(x)-2cos(x))

解

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

- 2 cos (2 x) + 2 sin (x)

解答ステップ

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

簡素化

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

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

和/差の法則を適用:

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

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

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

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

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

簡素化

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