derivative of a(sin(x-xcos(x)))

解

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

a x sin (x)

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

和/差の法則を適用:

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

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

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

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

= a (cos (x) - (cos (x) - x sin (x)))

簡素化

= a x sin (x)