An adaptive output feedback controller for nonlinear systems with nonlinearities depending on the first r (1 less than or equal to r less than or equal to n) derivatives of the output is proposed, The derivatives are estimated with a partial state high-gain observer, and the remaining states are handled using a backstepping method, Compared with methods based on full state high-gain observer, this approach improves robustness with respect to measurement noise and avoids overparameterization. Semiglobal tracking is proven under the assumption that the regressor is persistently exciting.