Summary: A general procedure is developed for calculating aerodynamic sensitivity coefficients using the full equations of inviscid fluid flow, where the focus of the work is the treatment of geometric shape design variables. Using an upwind cell-centered finite volume approximation to represent the Euler equations, sensitivity derivatives are determined by direct differentiation of the resulting set of coupled nonlinear algebraic equations that model the fluid flow. The technique is implemented and successfully tested in two dimensions for flow through a subsonic nozzle \((M_ \infty=0.85)\) and also a supersonic inlet \((M_ \infty=2.0)\). Specifically, the method is demonstrated by calculating the sensitivity of the aerodynamic loads (forces) on the interior walls of the nozzle/inlet to variations in the geometric parameters that define the shape. The sensitivity coefficients calculated using this approach compare very well with those calculated using the method of ``brute force'' (i.e., using finite differences to approximate the sensitivity derivatives) and are computationally less expensive to obtain.