  It is known that the vector space spanned by labeled rooted trees forms a
Hopf algebra. Let k be a field and let R be a commutative k-algebra. Let H
denote the Hopf algebra of rooted trees labeled using derivations D in Der(R).
In this paper, we introduce a construction which gives R a H-module algebra
structure and show this induces a differential algebra structure of H acting on
R. The work here extends the notion of a R/k-bialgebra introduced by Nichols
and Weisfeiler.
