In this work, we study various features of derivations on prime and semiprime rings. These rings are important in mathematics. We have shown, amongst other things, “that if R is indeed a semiprime ring, I denote a nonzero two-sided ideal of R, and f and g are derivations of R,” then they must meet the following condition: "if F(x)y+yg(x)=(0)for all x,y∈I,thence F(u)[x,y]=[x,y]g(u)=0" for every value of x,y∈I. In specifically, f and g are responsible for mapping I onto the middle of R. “If R represents a noncommutative prime ring, thence f=g=0 holds true for R. This statement may be thought of as an analogue of the Posner Lemma for a pair of derivations that meet this identity.”