Find the directional derivative of f=sqrt(xyz) at P(2,-1,-2) in the direction of v=i+2j-2k
The Attempt at a Solution
I calculate the gradient vector and obtain grad(f) at P= <1/2, 1, 1/2>
Then I find the unit vector of v, which is <1/3, 2/3, -2/3>
The directional derivative is the dot product of these two: 1/6 + 2/3 -2/6, which is 1/2. However, the answer is supposed to be -1/6 according to my textbook. Where's my mistake?