How can I prove "if $f$ is a finite Blaschke product then $f'(z) = 0$ if and only if $f'(\frac{1}{\bar{z}}) = 0$"?
A finite Blaschke product $f$ is a function of following type: $$f(z) = \alpha z^m \prod_{k=1}^{n} (\frac{z-z_k}{1-\bar{z_k}z}), |z_k| \not = 1$$