What is the derivative of e^{x^{-1}} ?

The derivative of e^{x^{-1}} is -(e^{1/x})/(x^2)

What is the first derivative of e^{x^{-1}} ?

The first derivative of e^{x^{-1}} is -(e^{1/x})/(x^2)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of e^{x^{-1}} ?
The derivative of e^{x^{-1}} is -(e^{1/x})/(x^2)
What is the first derivative of e^{x^{-1}} ?
The first derivative of e^{x^{-1}} is -(e^{1/x})/(x^2)