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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

tangent of e^x,\at x=ln(7)tangent of

e^{x}, at x = ln (7)

derivative of tan(e^{3t})+e^{tan(3t)}derivative of

tan (e^{3 t}) + e^{t a n (3 t)}

derivative of f(x)=7e^xcos(x)derivative of

f (x) = 7 e^{x} cos (x)

limit as x approaches 2 of sqrt(7-x)

x \to 2 lim (7 - x)

integral from 1 to infinity of x^{-1/3}

\int_{1}^{\infty} x^{- \frac{1}{3}} d x

Frequently Asked Questions (FAQ)

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