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

解

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

- x^{2} sin (x)

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

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

簡素化

2 x cos (x) - x^{2} sin (x) - 2 (sin (x) + x cos (x)) - (- 2 sin (x)) : - x^{2} sin (x)

= - x^{2} sin (x)