Summary: Let \(R\) be a prime ring and set \([x,y]_1=[x,y]=xy-yx\) for all \(x,y\in R\) and inductively \([x,y]_k=[[x,y]_{k-1},y]\) for \(k>1\). We apply the theory of generalized polynomial identities with automorphism and skew derivations to obtain the following result: Let \(R\) be a prime ring and \(I\) a nonzero ideal of \(R\). Suppose that \((\delta,\varphi)\) is a skew derivation of \(R\) such that \(\delta([x,y])=[x,y]_n\) for all \(x,y\in I\), then \(R\) is commutative.