derivative of sqrt(e^xsin(x))

解

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

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

解答ステップ

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

連鎖法則を適用:

\frac{1}{2 e ^{x} sin ( x )} \frac{d}{d x} (e^{x} sin (x))

= \frac{1}{2 e ^{x} sin ( x )} \frac{d}{d x} (e^{x} sin (x))

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

= \frac{1}{2 e ^{x} sin ( x )} (e^{x} sin (x) + cos (x) e^{x})

簡素化

\frac{1}{2 e ^{x} sin ( x )} (e^{x} sin (x) + cos (x) e^{x}) : \frac{e ^{x} sin ( x ) + e ^{x} cos ( x )}{2 e ^{x} sin ( x )}

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