Given an inner function Θ on the unit disc D, we study the boundedness of the differentiation operator which acts from the model subspace K _Θ = (ΘH ² ) ^⊥ of the Hardy space H ² , equipped with the BMOA-norm to some radial-weighted Bergman space. As an application, we generalize Peller’s inequality for Besov norms of rational functions f of degree n ≥ 1 having no poles in the closed unit disc D¯.