Generators and defining relations for the ring of differential operators on a smooth affine algebraic variety in prime characteristic

For the ring of differential operators D(O(X)) on a smooth affine algebraic variety X over a perfect field of characteristic p>0, explicit algebra generators and defining relations are found. A finite set of generators and a finite set of defining relations are given explicitly for the module DerK(O(X)) of derivations on the algebra O(X) of regular functions on the variety X.