Let R be a semiprime ring with a derivation d, λ a left ideal of R and k, n two positive integers. Suppose that [d(xn),xn]k = 0 for all x ∊ λ. Then [λ,R]d(R) = 0. That is, there exists a central idempotent e ∊ U, the left Utumi quotient ring of R, such that d vanishes identically on eU and λ(l — e) is central in (1 — e)U