derivative of e^{x/y}

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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