derivative of x/y+e^y

解

\frac{d}{d x} (\frac{x}{y} + e^{y})

\frac{y - x \frac{d y}{d x}}{y ^{2}} + e^{y} \frac{d y}{d x}

解答ステップ

\frac{d}{d x} (\frac{x}{y} + e^{y})

和/差の法則を適用:

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

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

\frac{d}{d x} (\frac{x}{y}) = \frac{y - x \frac{d y}{d x}}{y ^{2}}

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

= \frac{y - x \frac{d y}{d x}}{y ^{2}} + e^{y} \frac{d y}{d x}