In this talk, we demonstrate a fractional differentiability result for a nonlinear elliptic equation based on the perturbation method. We employ several regularity results such as Calderon-Zygmund estimates, gradient excess decay estimates, and higher differentiability to do so. By the end of this presentation, attendees will have a deeper understanding of how these techniques can be applied to achieve significant results in the study of nonlinear elliptic equations.