Directional Derivative of a Function in a Given Direction

[gtfitzpatrick]

Homework Statement

Find the Directional derivative of \varphi = x²+siny-xz in the direction of i+2j-2k at the point (1, \pi/2 , -3)

The Attempt at a Solution

u = i+2j-2k

\left|u\left| = \sqrt{1^2+2^2+(-2)^2} = 3


\Rightarrow u\hat{} = 1/3i+2/3j-2/3k

\nabla\varphi = (2x-z)i+(Cos y)j-xk

at the point (1, \pi/2 , -3)
u\hat{}\nabla\varphi = 5/3 + 0 +2/3 = 7/3

i think i have this right?

 

[Dick]

I think you have it right.

 

[gtfitzpatrick]

thanks a mill