Directional Derivative

A directional derivative is a measure of the rate of change of a multivariable function in a specific direction. While the partial derivatives of a function describe the rate of change in the direction of the coordinate axes, the directional derivative considers the rate of change in any arbitrary direction.

The directional derivative is calculated as the dot product of the gradient vector of the function and the unit vector in the desired direction. It provides insight into how a function behaves when moving along a particular path or in a specific direction, which is useful in various applications, including optimization problems, physics, and engineering.