Differentiation is the process of finding the rate of change of a function with respect to a single variable, while partial differentiation involves multiple independent variables. In the context of acceleration, g = GM/r^2 represents gravitational acceleration, and a = dv/dt defines acceleration as the change in velocity over time. Since introductory physics typically considers time as the sole independent variable, partial differentiation is not applicable. The discussion clarifies that both forms of differentiation serve different purposes based on the number of variables involved. Understanding these concepts is essential for grasping the fundamentals of motion and forces in physics.