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Popular >

derivative of e^{x^{-2}}

Solution

\frac{d}{d x} (e^{x^{- 2}})

Solution

- \frac{2 e ^{\frac{1}{x ^{2}}}}{x ^{3}}

Solution steps

\frac{d}{d x} (e^{x^{- 2}})

Apply the chain rule:

e^{x^{- 2}} \frac{d}{d x} (x^{- 2})

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

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

= e^{x^{- 2}} (- \frac{2}{x ^{3}})

Simplify

e^{x^{- 2}} (- \frac{2}{x ^{3}}) : - \frac{2 e ^{\frac{1}{x ^{2}}}}{x ^{3}}

= - \frac{2 e ^{\frac{1}{x ^{2}}}}{x ^{3}}

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Frequently Asked Questions (FAQ)

What is the derivative of e^{x^{-2}} ?
The derivative of e^{x^{-2}} is -(2e^{1/(x^2)})/(x^3)
What is the first derivative of e^{x^{-2}} ?
The first derivative of e^{x^{-2}} is -(2e^{1/(x^2)})/(x^3)