1. ## Directional Derivative

Find the directional derivative of f(x,y,z)=xy+z^2 at the point (1,2,3) in the direction of a vector making an angel of pi/4 with gradf(1,2,3).

2. ## Re: Directional Derivative

Originally Posted by mgwalker
Find the directional derivative of f(x,y,z)=xy+z^2 at the point (1,2,3) in the direction of a vector making an angel of pi/4 with gradf(1,2,3).
As $\displaystyle f$ is differentiable at $\displaystyle (1,2,3)$ the directional derivative in the direction of $\displaystyle u\;(||u||=1)$ is

$\displaystyle (\nabla f)(1,2,3)\cdot u=|| (\nabla f)(1,2,3) ||\;||u||\cos (\pi/4)=\ldots$