derivative of e^xsin(xcos(x))

解

\frac{d}{d x} (e^{x} sin (x) cos (x))

e^{x} sin (x) cos (x) + cos (2 x) e^{x}

解答ステップ

\frac{d}{d x} (e^{x} sin (x) cos (x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = sin (x) cos (x)

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

\frac{d}{d x} (e^{x}) = e^{x}

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

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