What is (\partial)/(\partial x)(e^{2/x}) ?

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

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(\partial)/(\partial x)(e^{2/x})

\frac{\partial}{\partial x} (e^{\frac{2}{x}})

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

Solution steps

\frac{\partial}{\partial x} (e^{\frac{2}{x}})

Apply the chain rule:

e^{\frac{2}{x}} \frac{\partial}{\partial x} (\frac{2}{x})

= e^{\frac{2}{x}} \frac{\partial}{\partial x} (\frac{2}{x})

\frac{\partial}{\partial x} (\frac{2}{x}) = - \frac{2}{x ^{2}}

= e^{\frac{2}{x}} (- \frac{2}{x ^{2}})

Simplify

e^{\frac{2}{x}} (- \frac{2}{x ^{2}}) : - \frac{2 e ^{\frac{2}{x}}}{x ^{2}}

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

\int_{3}^{\infty} 1

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