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Popular >

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

Solution

\frac{d}{d 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}}

Popular Examples

integral of (x^3)/(x^2-x)

\int \frac{x ^{3}}{x ^{2} - x} d x

derivative of (1+1/x ^{1/x})

\frac{d}{d x} ((1 + \frac{1}{x})^{\frac{1}{x}})

(\partial)/(\partial x)(xysqrt(x^2+y^2))

\frac{\partial}{\partial x} (x y x^{2} + y^{2})

integral of 3xsin(5x)

\int 3 x sin (5 x) d x

area x=9y^2,x=28+2y^2 area

x = 9 y^{2}, x = 28 + 2 y^{2}

Frequently Asked Questions (FAQ)

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