  Representing an atom by a solid sphere in $3$-dimensional Euclidean space, we
get the space-filling diagram of a molecule by taking the union. Molecular
dynamics simulates its motion subject to bonds and other forces, including the
solvation free energy. The morphometric approach [HRC13,RHK06] writes the
latter as a linear combination of weighted versions of the volume, area, mean
curvature, and Gaussian curvature of the space-filling diagram. We give a
formula for the derivative of the weighted mean curvature. Together with the
derivatives of the weighted volume in [EdKo03], the weighted area in [BEKL04],
and the weighted Gaussian curvature [AkEd19], this yields the derivative of the
morphometric expression of the solvation free energy.
