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)
|
