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}}

\int \frac{x + 1}{x ^{2} + x + 1} d x

\frac{d y}{d t} + 3 y = 11, y (0) = 1

\int \frac{- 4 x}{2 x + 1} d x

y^{^{''}} - 2 y^{^{'}} + 2 y = 6

x \to \infty lim (1 - \frac{1}{x})

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