Differential commutator identities

I.N. Herstein proved that if R is a prime ring satisfying a differential identity , with d a nonzero derivation of R, then R embeds isomorphically in M2(F) for F a field. We consider a natural generalization of this result for the class of polynomials En(X)=[En-1(x1,…,xn-1),xn]. Using matrix computations, we prove that if R satisfies a differential identity , or with some restrictions, then R must embed in M2(F), but that differential identities using [[En,Em],Es] with m,n,s>1 need not force R to embed in M2(F). These results hold if the expressions are identities for a noncommutative Lie ideal of R, rather than for R itself.