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}}

\frac{d}{d x} ((1 - x^{\frac{2}{3}})^{\frac{3}{2}})

x^{2} + 7 y^{2} = 7

\frac{d}{d x} (\frac{5 - cosh ( x )}{9 + cosh ( x )})

\frac{d}{d x} (\frac{( x - a ) ( b - x )}{x ^{2}})

\int \frac{8 e ^{8 s}}{3 + e ^{8 s}} d s

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)