directional derivative, derivation of

Let f(x,y) be a function where x=x(t) and y=y(t). Let r=a𝐢^+b𝐣^ be the vector in the desired direction. The line through this vector is given parametrically by:


The derivativePlanetmathPlanetmath of f with respect to t is as follows:


But from the equation of the line, we know that dxdt=a and dydt=b so the derivative becomes:


Title directional derivativeMathworldPlanetmath, derivation of
Canonical name DirectionalDerivativeDerivationOf
Date of creation 2013-03-22 15:25:22
Last modified on 2013-03-22 15:25:22
Owner apmc (9183)
Last modified by apmc (9183)
Numerical id 7
Author apmc (9183)
Entry type Derivation
Classification msc 26B12
Classification msc 26B10