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Homework Help: Directional derivative and gradient vector

  1. Mar 16, 2007 #1
    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 of v=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 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?
  2. jcsd
  3. Mar 16, 2007 #2


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    Homework Helper
    Gold Member

    Your mistake lies in your calculation of [tex]\vec\nabla f[/tex]

    Its should be: [tex]\vec\nabla f = <1/2, -1, -1/2>[/tex]

    Check your work for that part. Other than that everything else looks good. I get -1/6 for the directional derivative with that gradient. Good Luck!

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