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}}

\frac{d}{d x} (3 x (6 x - 5 x^{2}))

\frac{d}{d x} ((80 e^{- \frac{x}{10}}) - 40 x)

x^{2} - 2 x, 3 x + 6

x \to 3 lim (- 3)

y = (\frac{x ^{2} + 2}{x ^{2} - 2})^{6}

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)