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## Homework Statement

Find the directional derivative of f=sqrt(xyz) at P(2,-1,-2) in the direction of

**v**=

**i**+2

**j**-2

**k**

## 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?