The last years have seen a growing interest from mathematicians in Mahler functions. This class of functions includes the generating series of the automatic sequences. This talk is concerned with the following problem: a set of Mahler functions $u_{1},...,u_{n}$ being given, are $u_{1},...,u_{n}$ and their successive derivatives algebraically independent? We will give a general criterion ensuring an affirmative answer to this question and will give an application to the generating series attached to the so-called Baum-Sweet and Rudin-Shapiro automatic sequences. Our approach relies of the parametrized difference Galois theory. This is a joint work with T. Dreyfus and C. Hardouin.