Pointwise differentiability of higher-order for distributions

For distributions, we build a theory of higher order pointwise differentiability comprising, for zero, {\L}ojasiewicz's notion point value. Results include Borel regularity differentials, rectifiability the associated jets, Rademacher-Stepanov type theorem, and Lusin approximation. A substantial part this development is new also zeroth order. Moreover, establish Poincar\'e inequality involving natural norms negative differentiability. As corollary, characterise in terms values distributional partial derivatives.