What is the derivative of f(z)=e^{z/((z-1))} ?

The derivative of f(z)=e^{z/((z-1))} is -(e^{z/(z-1)})/((z-1)^2)

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

The first derivative of f(z)=e^{z/((z-1))} is -(e^{z/(z-1)})/((z-1)^2)

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derivative of

f (z) = 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 y}{d x} = \frac{x}{2 y ^{2}}

x \to 8 + lim (\frac{7 - x}{8 - x})

\frac{d y}{d x} = \frac{cos ( 11 x )}{e ^{11 y}}

x \to 5 lim (\frac{3}{( x - 5 ) ^{2}})

1 - x

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