# Directional Derivative

The directional derivative  is the rate at which the function  changes at a point in the direction . It is a vector form of the usual derivative, and can be defined as
 (1) (2)
where  is called "nabla" or "del" and  denotes a unit vector.
The directional derivative is also often written in the notation
 (3) (4)
where  denotes a unit vector in any given direction and  denotes a partial derivative.
Let  be a unit vector in Cartesian coordinates, so
 (5)
then

 (6)