Directional Derivative

Rate of change of a multivariable function in the direction of the unit vector .

Directional derivative of in the direction is:

If and are continuous at , then has a directional derivative in any direction .

Also the directional derivative can be written as:

Gradient

Denoted by . Can be extended for functions with more inputs.

The is the “del operator”.

Maxmimum of Directional Derivative

Maximum value of the directional derivative is and occurs when the gradient vector and has the same direction.