Final answer:
The directional derivative measures how fast a function changes in a specific direction at a point.
Step-by-step explanation:
The directional derivative at a point in a given direction is the rate at which the function changes in that direction at that point. It measures how fast the function is changing along a specific direction. To approximate the directional derivative, we can use the gradient of the function.
The directional derivative is given by the dot product of the gradient vector and the unit vector in the direction:
D = ∇f · u
where ∇f is the gradient of the function and u is the unit vector in the direction.