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 fieldu= [2,-1,1].

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

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?