Let k be a commutative ring, A a commutative k -algebra and D the filtered ring of k -linear differential operators of A . We prove that: (1) The graded ring gr D admits a canonical embedding θ into the graded dual of the symmetric algebra of the module Ω A / k of differentials of A over k , which has a canonical divided power structure. (2) There is a canonical morphism ϑ from the divided power algebra of the module of k -linear Hasse–Schmidt integrable derivations of A to gr D . (3) Morphisms θ and ϑ fit into a canonical commutative diagram.