# Directional derivative

1. Jan 31, 2010

### gtfitzpatrick

1. The problem statement, all variables and given/known data

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

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?

2. Jan 31, 2010

### Dick

I think you have it right.

3. Jan 31, 2010

### gtfitzpatrick

thanks a mill