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}}})

Simplify

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

= \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}}

x \to 3 lim (\frac{7 x ^{2} - 3 x}{x})

\frac{1}{4} (\frac{d y}{d t}) + 10 y = 5

\int sec^{2} (x t a) n^{2} x d x

f (x) = x^{3} - \frac{3}{2} x^{2} + x, at x = 1

n = 2 \sum \infty \frac{( - 1 ) ^{n}}{n ln ( n )}

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)