  For a grand canonical ensemble of classical point-like particles at
equilibrium in continuous space we investigate the functional relationship
between a stable and regular pair potential describing the interaction of the
particles and the corresponding molecular distribution functions. For certain
admissible perturbations of the pair potential and sufficiently small activity
we rigorously establish Frechet differentiability with respect to the supremum
norm in the image space -- both for bounded domains and in the thermodynamical
limit.
