An adjoint-based methodology is developed and validated to numerically estimate the sensitivities of a semi-analytical model for computing the broadband noise associated to the interaction between a turbulent boundary layer and a two-dimensional airfoil trailing-edge. To this end, an acoustic objective function based on Amiet’s theory in combination with a semi-empirical wall pressure spectrum model is proposed. The steady-state boundary layer integral quantities required by the semi-empirical model are obtained using Reynolds-Averaged Navier-Stokes simulations. After validation of this methodology on a NACA0012 airfoil, the model sensitivities are obtained numerically using algorithmic differentiation of computer programs. The sensitivities to camber and thickness, computed with the associated adjoint solver, are compared to finite differences evaluations on an asymmetric OAT15 airfoil at subsonic and transonic speeds. The results show that the model is most sensitive to camber and thickness variations close to the trailing-edge, especially at transonic speed. The adjoint method proves much more computationally efficient in obtaining the sensitivities than finite differences and offers perspectives for multi-disciplinary propeller blade shape optimization.