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Popular >

derivative of e^{1/(x-1})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{1}{x - 1}) = - \frac{1}{( x - 1 ) ^{2}}

= e^{\frac{1}{x - 1}} (- \frac{1}{( x - 1 ) ^{2}})

Simplify

e^{\frac{1}{x - 1}} (- \frac{1}{( x - 1 ) ^{2}}) : - \frac{e ^{\frac{1}{x - 1}}}{( x - 1 ) ^{2}}

= - \frac{e ^{\frac{1}{x - 1}}}{( x - 1 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

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