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

解

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

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

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

簡素化

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

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