Answer
$f'(z)=-\frac{e^{\frac{z}{(z-1)}}}{(z-1)^{2}}$
Work Step by Step
Take the derivative of the function $f(z)=e^{\frac{z}{(z-1)}}$.
$f'(z)=\frac{d}{dz}[e^{\frac{z}{(z-1)}}]$
Apply chain rule.
Hence, $f'(z)=-\frac{e^{\frac{z}{(z-1)}}}{(z-1)^{2}}$
