Math Is Fun Forum

sarsalan

Member

Registered: 2008-11-03

Posts: 16

Directional Derivatives

Q 1. Let f(x,y) = x^2 - 4xy?
a. Find the gradient of f at the point P(1,2) .
b. Find directional derivative of f at P(1,2) at in the direction from P(1,2) to Q(2,5)

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Directional Derivatives

Gradient is defined as a vector with the components being the partial derivatives.

Directional Derivative is defined as the dot product of the gradient and a unit vector.

This is the gradient of F at (1,2). (thanks Daniel123 for providing the code )

So now you have the gradient. To find the directional derivative, find the vectors from the two points given. Normalize it and then the directional derivative will be the dot product of the gradient and this unit vector.

Last edited by LuisRodg (2008-11-09 03:37:59)