When applying the elastic anisotropic wave equation operator for spatially varying media, several first order derivatives have to be calculated in the process. The wave equation can formally be split into two components such that derivatives are taken with respect to medium parameters and with respect to the propagating wave field. Splitting the wave equation operator allows us to adapt derivative operators to the physical quantities to be differentiated. In particular the adaption can be guided by special properties of the observable quantity. Practical problems can arise since in general anisotropic media the derivated quantities have to be interpolated back to collocation points.