en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

\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}}

Popular Examples

integral of 3x^2-2x+1

\int 3 x^{2} - 2 x + 1 d x

dy+(2xy-4e^{-x^2})dx=0

d y + (2 x y - 4 e^{- x^{2}}) d x = 0

slope of (4,1),(3,1)slope

(4, 1), (3, 1)

(x+y)^2dx+(2xy+x^2-6)dy=0

(x + y)^{2} d x + (2 x y + x^{2} - 6) d y = 0

derivative of (xlog_{2}(x))^2 derivative of

(x lo g_{2} (x))^{2}

Frequently Asked Questions (FAQ)

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)