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Popular >

Find the Derivative - d/dx e^(1/x)

Solution

derivative of

\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}})

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}}

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\frac{d}{d x} y = 8 x

Evaluate the Derivative at @POINT y=2x^3-5x , (1,-3)derivative of

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Frequently Asked Questions (FAQ)

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