The directional derivative del _u f(x_0, y_0, z_0) is the rate at which the function f(x, y, z) changes at a point (x_0, y_0, z_0) in the direction u. It is a vector form of the usual derivative, and can be defined as del _u f | congruent | del f·u/( left bracketing bar u right bracketing bar ) | = | lim_(h->0) (f(x + hu^^) - f(x))/h, where del is called "nabla" or "del" and u^^ denotes a unit vector.

derivative | gradient | vector derivative