Boundary behavior of derivatives of conformal mappings of simply connected domains

Conformal mappings of simply connected domains $G$ on a disc or a halfplane are considered in the case when boundaries consist of smooth boundary arcs $\Gamma$ reachable from inside of $G$. Sufficient conditions for existence of angular limit of the derivative of such mappings and its boundedness at some given boundary point are found. A sufficient condition of existence of a bounded derivative on the region's boundary is given as a corollary.