This paper proposes a technique to extract two-dimensional multiple phase derivatives (strains, slopes, and shearing strains) from a single frame of the interference fringe pattern recorded in an optical setup with multiple illumination beams. In the proposed method, the interference field is modeled as a multicomponent complex sinusoid in an analysis window around each pixel. The frequencies of these sinusoids provide the estimates of the spatially varying phase derivatives. Matrix enhancement and matrix pencil-based technique is utilized to accurately estimate the multiple frequencies. A numerical example is provided to test the performance of the proposed method in the presence of noise. Experimental results are given to substantiate its applicability in the simultaneous estimation of multiple phase derivatives in a multiwave digital holographic interferometry setup.