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

解

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

x^{2} cos (x) + 3 x sin (x) - cos (x)

解答ステップ

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

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

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

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

簡素化

2 x sin (x) + cos (x) x^{2} - (cos (x) - x sin (x)) : x^{2} cos (x) + 3 x sin (x) - cos (x)

= x^{2} cos (x) + 3 x sin (x) - cos (x)