  We define an analogue of the Fox derivatives for differential polynomial
algebras and give a criterion for differential algebraic dependence of a finite
system of elements. In particular, we prove that differential algebraic
dependence of a finite set of elements of a differential polynomial algebra
over a constructive differential field $k$ of characteristic zero is
algorithmically recognizable. Using a representation of free Novikov algebras
by differential polynomials we also give a criterion of Novikov dependence of a
finite system of elements of free Novikov algebras.
