University Mathematics Handbook (2015)

VII. Differential Calculus of Multivariable Functions

Chapter 7. Directional Derivative

a.  A directional derivative of function in the direction of unit vector at point is , when tends to along the ray originating from in the direction of .

It is denoted as , or .

b.  If function belongs to class in the neighborhood of , then

c.  A directional derivative describes the rate of change of the function at a certain point in a certain direction.

d.  The maximum rate of change of function on is in the direction of gradient vector (see IX.7):

e.  The maximum value of directional derivative is in the direction of and equals