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Homework Help: Directional derivative question

  1. Mar 31, 2014 #1
    1. The problem statement, all variables and given/known data
    rate of change of [itex] f(x,y) = \frac{x}{(1+y)} [/itex] in the direction (i-j) at the point (0,0)

    2. Relevant equations

    3. The attempt at a solution
    [itex] ∇f(x,y) = \frac{1}{(y+1)}\hat{i} - \frac{x}{(y+1)^2}\hat{j} [/itex]

    [itex]D_u = ( f_x, f_y) \bullet ( 1, -1 )[/itex]

    [itex]D_u = \frac{(y+x+1)}{(y+1)^2} [/itex]

    Wolfram and the answer sheet is telling me that there should be a [itex]\sqrt{2}[/itex] in the denominator, but I can't figure out where it comes from, thanks.
    Last edited: Mar 31, 2014
  2. jcsd
  3. Mar 31, 2014 #2


    User Avatar
    Science Advisor
    Homework Helper

    The vector you want to dot the grad with should be a unit vector pointed in the direction i-j. That's what 'in the direction' means.
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