scalar/vector field question

hey guys, I've been asked to consider the scalar field:

f(x,y,z) = xy + xz + yz

After finding grad f, I am asked to find the directional derivative of f at the point P (1,1,1) along the vector field **u** = [2,-1,1].

What confuses me is finding the directional derivative of f along the vector *field* **u**... do i just calculate the dot product of grad f and the unit vector of **u**?

grad f = (y+z)**i** + (x+z)**j** + (x+y)**k**

The answer i got when performing the calculations the way I believe to be correct is $\displaystyle 2\sqrt{6}/3$, does anybody know if this is correct?