The Kundu-Eckhaus equation and the derivative nonlinear Schrodinger equation describe various physical processes in nonlinear optics, plasma physics, fluid mechanics, magneto-hydrodynamic equation in the presence of the Hall Effect. Thus, closed form solutions of these equations are very important to realize the obscurity of the phenomena. The modified simple equation (MSE) method is highly effective and competent mathematical tool to examine closed form wave solutions of nonlinear evolution equations (NLEEs) arising in mathematical physics, applied mathematics and engineering. In this article, the MSE method is suggested and executed to construct closed form wave solutions of the above-mentioned equations involving parameters. When the parameters receive special values, impressive solitary wave solutions are derived from the exact solutions.