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

Kaplan, W. "The Directional Derivative." §2.14 in Advanced
Calculus, 4th ed. Reading, MA: Addison-Wesley, pp. 135-138, 1991.Morse,
P. M. and Feshbach, H. "Directional Derivatives." In Methods
of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 32-33, 1953.