Commutators with power central values on a Lie ideal

Let R be a prime ring of characteristic not equal 2 with a derivation d not equal 0, L a noncentral Lie ideal of R such that [d(u), u](n) is central, for all u is an element of L. We prove that R must satisfy s(4) the standar d identity in 4 variables. We also examine the case R is a 2-torsion free s emiprime ring and [d([x, y]), [x, y]](n) is central, for all x, y is an ele ment of R.