1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 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


    User Avatar
    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).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook