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Partial derivative

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data

    find the partial derivative of f(x,y)=(x^3+y^3)^(1/3) with respect to x and evaluate at (0,0)

    2. Relevant equations

    3. The attempt at a solution
    i found the general partial derivative with respect to x is (x^2)*(x^3+y^3)^(-2/3)
    if i plug in the point i would get zero at the bottom
    so i used the limit thing which is the limit of (f‘(x+h,y)-f(x,y))/h as h approaches infinite.
    then i substitute , i got something like lim (((x+h)^3+y^3)^(1/3)-(x^3+y^3)^(1/3))/h as h approaches infinite. then i plug in x=0, y=0, i got lim ((h^3)^(1/3))/h as h approaches infinite which is just 1
    i am not sure about what i did is right or not
  2. jcsd
  3. Oct 12, 2009 #2


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    Science Advisor

    Your partial derivative is correct, but the value at (x,y)=(0,0) depends on how you approach this point. It is 1 if you first set y=0 with x positive, and then take the limit as x->0.

    Bad question. Complain to your instructor. Seriously.
  4. Oct 12, 2009 #3
    The partial derivative is simply not defined at (0,0).
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