derivative f(x)=e^{1/x}

解

導関数

f (x) = e^{\frac{1}{x}}

- \frac{e ^{\frac{1}{x}}}{x ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

e^{\frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{e ^{\frac{1}{x}}}{x ^{2}}

= - \frac{e ^{\frac{1}{x}}}{x ^{2}}