This article deals with the dynamic response optimization of mechanical systems, based on the computation of independent state sensitivities. Specifically, the dynamic behavior of a coach is analyzed in detail so as to improve its response in terms of handling and ride comfort behaviors. To that end, the coach is modeled as an 18DOF multibody system, whose equations of motion are posed using an efficient dynamic formulation based on Maggi's equations. Next, a direct-automatic differentiation approach for the computation of independent state sensitivities is applied. This allows one to quantify the effect of 19 design parameters on the vehicle dynamic response and to compute the design sensitivities or objective function gradients. Finally, handling and ride comfort objective functions are defined and are used to carry out a multi-objective suspension design optimization process, improving the vehicle response by 70% in an effective yet automatic way.