What is the derivative of f(x)=e^{1/x} ?

The derivative of f(x)=e^{1/x} is -(e^{1/x})/(x^2)

What is the first derivative of f(x)=e^{1/x} ?

The first derivative of f(x)=e^{1/x} is -(e^{1/x})/(x^2)

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derivative

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

Solution steps

\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}}

What is the derivative of f(x)=e^{1/x} ?
The derivative of f(x)=e^{1/x} is -(e^{1/x})/(x^2)
What is the first derivative of f(x)=e^{1/x} ?
The first derivative of f(x)=e^{1/x} is -(e^{1/x})/(x^2)