The theory applying to dynamic programming has furnished a useful set of techniques for the analysis of many types of sequential models. This theory, however, has not yielded heretofore much information about the differentiability properties of optimal solutions. This aspect is of particular interest as regards the qualitative analysis of optimal paths, where differentiable methods are often called into play. This paper shows roughly that if the objective is twice continuously differentiable and strongly concave, then any interior optimal path is continuously differentiable with respect to the initial state.