$ (f^{-1})'(\zeta) \neq 0 $ holds for every $ \zeta \in \partial D $?

Question

Let $ \Omega \subseteq \mathbb{R}^2 $ be simply connected and bounded domain with $ \partial \Omega \in C^2 $, $ D $ denotes the unit disc, $ f $ be the conformal mapping from $\Omega $ to $ D $, then $ (f^{-1})'(\zeta) \neq 0 $ holds for every $ \zeta \in \partial D $? Could anyone recommend some reference for this proposition?