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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (- \frac{1}{x ^{2}}) = \frac{2}{x ^{3}}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

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