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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Simplify

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

= \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}}

Graph

Popular Examples

limit as x approaches 0 of 10^x

x \to 0 lim (1 0^{x})

limit as x approaches 3 of (x^2-2)/(3-x)

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

tangent of y=(x^3-4x)^{10}

t an g e n t y = (x^{3} - 4 x)^{10}

derivative of 5/2 x

\frac{d}{d x} (\frac{5}{2} x)

tangent of 3/(sin(x)+cos(x))

t an g e n t \frac{3}{sin ( x ) + cos ( x )}

Frequently Asked Questions (FAQ)

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)