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)

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derivative of

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

- \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}}

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)