1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Directional derivative

  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


    User Avatar
    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!

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Directional derivative
  1. Directional derivatives (Replies: 11)