derivative of e^{(-1/x})

解

\frac{d}{d 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}})

簡素化

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

= \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}}