This letter describes the first derivatives estimation of nonlinear parameters through an embedded identifier in the hybrid system by using a feed-forward neural network (FFNN). The hybrid systems are modelled by the differential-algebraic-impulsive-switched (DAIS) structure. The FFNN is used to identify the full dynamics of the hybrid system. Moreover, the partial derivatives of an objective function J with respect to the parameters are estimated by the proposed identifier. Then, it is applied for the identification and estimation of the non-smooth nonlinear dynamic behaviors due to a saturation limiter in a practical engineering system.