Numerical optimization strategies iteratively adjust design parameters in a parameterized problem to achieve an optimized performance. In gradient-based optimization strategies, the design variable update is based on sensitivity information. To reduce computation time, novel methods to compute the sensi- tivities, such as direct differentiation or the adjoint method, are desired. However, for these approaches the sensitivities depend on the governing equations of the system, which can significantly increase the complexity of the sensitivity analysis. In finite deformation contact mechanics [2], the geometric non- linearity, as well as nonlinearity stemming from the contact search, must be considered. In addition, for frictional contact problems [3], the governing equations are path-dependent. Therefore, the entire load path must be considered in the sensitivity analysis. We present consistent sensitivity analysis for state-of-the-art 3D finite deformation mortar frictional contact mechanics problems [1]. Since we have chosen topology optimization as an exemplary application, we will present the sensitivity analysis using the adjoint method, which is more efficient than the direct differentiation approach for a large number of design parameters. Nevertheless, the insights presented can straightforwardly be transferred to the direct differentiation approach. We derive the sensitivity analysis, including consistent analytical linearization, for all three common contact enforcement approaches in the mortar setting, i.e., the Lagrange multiplier method, the penalty method, and the augmented Lagrangian method. Numerical examples that utilize the newly developed sensitivity analysis strategies are presented. These examples demonstrate the ne- cessity to incorporate frictional mechanics into the process when designing structures using numerical optimization. [1] Rinderer, L., Popp, A. and Gee, M.W., Topology optimization of 3D finite deformation mortar frictional contact problems using adjoint sensitivities, Comp. Meth. Appl. Mech. Engrg., 449, 118507, 2026. [2] Popp, A., Gee, M.W. and Wall, W.A., A finite deformation mortar contact formulation using a primal– dual active set strategy, Int. J. Numer. Methods Eng., 79, 1354-1391, 2009. [3] Gitterle, M., Popp, A., Gee, M.W. and Wall, W.A., Finite deformation frictional mortar contact using a semi-smooth Newton method with consistent linearization, Int. J. Numer. Methods Eng., 84, 543-571, 2010.