(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the directional derivative of f=sqrt(xyz) at P(2,-1,-2) in the direction ofv=i+2j-2k

3. 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 ofv, 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?

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# Directional derivative and gradient vector

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