The systematic design of a robust output tracking algorithm for a feedback linearizable system with unmatched uncertainties is presented. The proposed technique is based on a backstepping procedure to construct a time-varying singularly perturbed system and the underlying theoretical approach by the Lyapunov theory. The main result is that a dynamically parametrized state feedback is developed to cancel the output tracking error. Finally, an illustrative example through a chemical reactor system is given to demonstrate the utilization of the approach developed in this paper.