  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 thermodynamical limit of the Ursell or pair correlation
function. For certain admissible perturbations of the pair potential and
sufficiently small activity we rigorously establish Frechet differentiability
of the Ursell function in the $L^1$ norm. Furthermore, concerning the
thermodynamical limit of the pair distribution function we explicitly compute
its Fr\'echet derivative as a sum of a multiplication operator and an integral
operator.
