We establish sufficient conditions for 3-prime near-rings to be commutative rings. In particular, for a 3-prime near-ring R with a derivation d, we investigate conditions such as d([U,V])⊆Z(R)\documentclass[12pt]{minimal}
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\begin{document}$$d([U,V])\subseteq Z(R)$$\end{document}, d(U)⊆Z(R)\documentclass[12pt]{minimal}
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\begin{document}$$d(U)\subseteq Z(R)$$\end{document}, xod(R)⊆Z(R)\documentclass[12pt]{minimal}
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\begin{document}$$x_{o}d(R)\subseteq Z(R)$$\end{document}, and Uxo⊆Z(R)\documentclass[12pt]{minimal}
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\begin{document}$$Ux_{o}\subseteq Z(R)$$\end{document}. As a by-product, we generalize and extend known results related to rings and near-rings. Furthermore, we discuss the converse of a well-known result in rings and near-rings, namely: if x∈Z(R)\documentclass[12pt]{minimal}
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\begin{document}$$x\in Z(R)$$\end{document}, then d(x)∈Z(R)\documentclass[12pt]{minimal}
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\begin{document}$$d(x)\in Z(R)$$\end{document}. In addition, we provide useful examples illustrating our results.
