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