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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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}}

Simplify

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

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

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