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

解

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

2 e^{x} cos (x)

解答ステップ

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

和/差の法則を適用:

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

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

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

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

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

簡素化

= 2 e^{x} cos (x)