What is (\partial)/(\partial x)(e^{-1/x}) ?

The answer to (\partial)/(\partial x)(e^{-1/x}) is (e^{-1/x})/(x^2)

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(\partial)/(\partial x)(e^{-1/x})

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}}

- 3 x^{2} y + y^{^{'}} = - 9 x^{2}

\int_{- 8}^{0} 2 + 64 - x^{2} d x

y = \frac{2}{x - 2}, (4, 1)

\frac{d}{d t} (t^{2} + t)

\frac{d y}{d x} - \frac{9}{x} y = \frac{y ^{5}}{x ^{18}}, y (1) = 1

What is (\partial)/(\partial x)(e^{-1/x}) ?
The answer to (\partial)/(\partial x)(e^{-1/x}) is (e^{-1/x})/(x^2)