This paper presents a detailed mathematical derivation of the sensitivity derivatives for the structural dynamic, aeroelastic stability and response characteristics of a rotor blade in hover and forward flight. The formulation is denoted by the term semi-analytical approach, because certain derivatives have to be evaluated by a finite difference scheme. Using the present formulation, sensitivity derivatives for the structural dynamic and aeroelastic stability characteristics, were evaluated for both isotropic and composite rotor blades. Based on the results, useful conclusions are obtained regarding the relative merits of the semi-analytical approach, for calculating sensitivity derivatives, when compared to a pure finite difference approach.