In this paper, we investigate the properties and the precise solutions of the Mordukhovich derivatives of the set-valued metric projection operator onto some closed balls in some general Banach spaces. In the Banach space c, we find the properties of Mordukhovich derivatives of the set-valued metric projection operator onto the closed subspace c0. We show that the metric projection from C[0, 1] to polynormal with degree less than or equal to n is a single-valued mapping. We investigate its Mordukhovich derivatives and Gateaux directional derivatives.
