The Rigorous Coupled-Wave Analysis (RCWA) is a method to compute diffraction of a field by a given grating structure. Within various applications such as metrology, it is important to know how the field reacts to small perturbations in the grating. This behaviour can be expressed by the field derivatives with respect to a certain parameter. Approximations of these derivatives can be found by using finite differences where the field is computed for neighbouring values of the parameter and the difference gives the derivative. Unfortunately, RCWA computations involve solving eigenvalue systems which are computationally expensive. Therefore, a faster alternative is given which computes the derivatives by straightforward differentiating the relations within RCWA. Solving additional eigensystems is replaced by finding derivatives of eigenvalues and eigenvectors, which is less computationally expensive.