The effects of sensitivities on the performance of aerodynamic design optimization were evaluated. Sensitivities were obtained by both analytical and finite-difference approaches. A direct differentiation method was developed to analytically obtain sensitivities for the two-dimensional Euler equations using the material derivative concept of continuum mechanics. Several inverse design optimizations were performed to evaluate the merits of the analytical approach in comparison with the finite-difference approach. The results show that the analytical approach provides accurate sensitivities consistently, improves the convergence of the design cycle, and hence reduces the design cost.