In this paper, we introduce the concept of second order partial
derivatives in the extended sense for nonconvex functions and prove a formula
computing the extended Hessian in terms of the second order partial derivatives
in the extended sense. We show that the sum, difference, product, and quotient
of functions that are twice differentiable at a point are functions that are twice
differentiable at that point in the extended sense. We also show why the counterpart of the second order differentiability in the extended sense on Rn does not
appear in variational analysis.