Commuting product of generalized derivations on multilinear polynomials in prime rings

Let R be a prime ring of characteristic different from 2, U the Utumi quotient ring of R, C the extended centroid of R, F and G non-zero generalized derivations of R and f (x(1),..., x(n)) a multilinear polynomial over C. Suppose that f (x(1),..., x(n)) is not central valued on R, and R does not embed in M-2(K), the algebra of 2 x 2 matrices over a field K. We describe all possible forms of F and G in the case [f(g(f(r(1) ...r(n)))), f(r(1),...,r(n))] = 0 for any r(1),..., r(n) is an element of R.