derivative-x^2sin(x)+4xcos(x)+2sin(x)

解

導関数

- x^{2} sin (x) + 4 x cos (x) + 2 sin (x)

- x^{2} cos (x) - 6 x sin (x) + 6 cos (x)

解答ステップ

\frac{d}{d x} (- x^{2} sin (x) + 4 x cos (x) + 2 sin (x))

和/差の法則を適用:

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

= - \frac{d}{d x} (x^{2} sin (x)) + \frac{d}{d x} (4 x cos (x)) + \frac{d}{d x} (2 sin (x))

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

\frac{d}{d x} (4 x cos (x)) = 4 (cos (x) - x sin (x))

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

= - (2 x sin (x) + cos (x) x^{2}) + 4 (cos (x) - x sin (x)) + 2 cos (x)

簡素化

- (2 x sin (x) + cos (x) x^{2}) + 4 (cos (x) - x sin (x)) + 2 cos (x) : - x^{2} cos (x) - 6 x sin (x) + 6 cos (x)

= - x^{2} cos (x) - 6 x sin (x) + 6 cos (x)