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
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)
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where 
is called "nabla" or "del" and 
denotes a unit vector.
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.
denotes a unit vector in any given direction and denotes a partial derivative.
Let 
be a unit vector in Cartesian coordinates, so
be a unit vector in Cartesian coordinates, so |
(5)
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then
 |
(6)
|