Exceptional sets for the derivatives of Blaschke products

is the Nevanlinna characteristic of f [13]. Meromorphic functions of finite order have been extensively studied and they have numerous applications in pure and applied mathematics, e.g. in linear differential equations. In many applications a major role is played by the logarithmic derivative of meromorphic functions and we need to obtain sharp estimates for the logarithmic derivative as we approach to the boundary [7, 8]. In particular, the following result for the rate of growth of meromorphic functions of finite order in the unit disc has application in the study of linear differential equations [10, Theorem 5.1].