(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Directional derivative and gradient vector

**Physics Forums | Science Articles, Homework Help, Discussion**