Gradient of a Function

The gradient of a function represents the rate and direction of the maximum rate of increase of the function. It is denoted as ∇f and comprises the partial derivatives of the function with respect to its variables x_1, x_2, ..., x_n. In a three-dimensional space, the gradient points in the direction of the steepest ascent of the function. The gradient is fundamental in vector calculus and frequently used in optimization and physics to represent forces, velocity fields, and other vector quantities.