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Popular >

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

Solution

derivative of

e^{\frac{z}{z - 1}}

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(e^{3x}cos(4y))

\frac{\partial}{\partial x} (e^{3 x} cos (4 y))

integral of 1/(csc(x))

\int \frac{1}{csc ( x )} d x

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\int_{0}^{2} π (e^{x})^{2} d x

derivative of y=x-cos^2(x)derivative of

y = x - cos^{2} (x)

area y=(15)/(x^3+2x),1,2 area

y = \frac{15}{x ^{3} + 2 x}, 1, 2

Frequently Asked Questions (FAQ)

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