This study aims to analyze the derivatives of a two-variable function and visualize the results in the form of a 3D graph using Python. Derivatives of two-variable functions are essential in multivariate analysis, such as optimization and surface analysis. The study uses Visual Studio Code as the Integrated Development Environment (IDE) to develop and run Python code, utilizing libraries such as NumPy, SymPy, and Matplotlib for mathematical computations and visualization. The first step involves programming partial derivatives of a two-variable function using SymPy. Subsequently, the derivative results are visualized in 3D using Matplotlib to illustrate the surface and gradient of the function. The goal of this research is to provide a deeper understanding of the application of derivatives in two-variable functions and the benefits of visualization in analyzing these derivative results. The findings are expected to contribute to the fields of mathematics education and numerical computation applications.