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Directional Derivative

  1. Oct 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the directional derivative of f at P in the direction of a.
    f(x,y)=y2lnx; P(1,4); a= -3i + 3j

    2. Relevant equations

    3. The attempt at a solution
    I first normalized the vector and got an = -3/(18)^1/2 + 3/(18)^1/2
    Then i took the partial derivative and multiplied it by the vector
    y2/X(-3/181/2) + 2(y)lnx(3/181/2
    Ln(1) = 0 so the whole right side is gone, and after i plug in 1 and 4 on the right side i get -16/21/2. The answer should be -8/21/2. I've done 5 problems like this now and each time i'm off by a negative or a factor or something like that. What am i doing wrong?
  2. jcsd
  3. Oct 7, 2008 #2


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    I get -16/sqrt(2) as well. Are you sure the answer wasn't -8*sqrt(2)? That would be the same thing you have.
  4. Oct 7, 2008 #3
    Thanks, i just went back and checked the back of the book, the answer is supposed to be -8*sqrt(2) not -8/sqrt(2). Also i didn't notice that -16/sqrt(2) is the same thing as -8*sqrt(2). Thanks for the help.
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