derivative of axcos(2x+bxsin(2x))

解

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

a (cos (2 x) - 2 x sin (2 x)) + b (sin (2 x) + 2 x cos (2 x))

解答ステップ

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

和/差の法則を適用:

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

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

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

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

= a (cos (2 x) - 2 x sin (2 x)) + b (sin (2 x) + 2 x cos (2 x))