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Sensitivity analysis of large displacement multi-body two-dimensional contact problems with friction is developed in the paper. The incremental (path-dependent) sensitivity problem is derived by direct differentiation of the discretized equations governing the direct problem. In view of finite deformations, due attention is paid to spatial and nominal contact tractions and to proper formulation of the contact laws within the penalty approach. For these reasons an extended node-to-segment contact element is used to model the frictional contact interactions. As the finite elasto-plastic deformations of the contacting bodies are considered, the numerical procedures for computation of all the necessary characteristic formulae of the solid elements (for both the direct and the sensitivity problem) are automatically derived and generated using the symbolic algebra package AceGen. Numerical examples of shape and parameter sensitivity analysis illustrate the approach.