Because when you differ, you want to know the difference in energy between two states that feature different thermodynamic conditions. The `A` is energy given a particular N,V,T tuple. That means that `A` actually depend on that tuple and when you want to compute the difference in `A` between two different NVT tuples you have to define `A` as a function of NVT:

dA = -pdV + SdT + Xdmu