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 Derivatives question

  1. Oct 26, 2008 #1
    1. The problem statement, all variables and given/known data

    Evaluate the partial derivatives ∂f/∂x and ∂f/∂y at the origin (0,0), where:

    f(x,y) = ((xy)^3/2)/(x^2 + y^2) if (x,y) ≠ (0,0);
    and f(0,0) = 0.

    2. Relevant equations

    ∂f/∂x(x0,y0) = lim(h->0) [(f(x0+h, y0) - f(x0, y0)) / h]

    ∂f/∂y(x0,y0) = lim(h->0) [(f(x0, y0+h) - f(x0, y0)) / h]

    3. The attempt at a solution

    When I tried to use the definition for ∂f/∂x I got lim(h->0) (0/h^3), and the same result for ∂f/∂y. Is it correct to say therefore the partial derivatives at the origin are zero?
  2. jcsd
  3. Oct 26, 2008 #2


    User Avatar
    Science Advisor

    Yes, the partial derivative with respect to x at (0,0) is taken as x= h approaches 0 and y= 0. That means that the numerator is is 0 for all h so the "difference quotient" is 0 for all non-zero h. The limit, as h goes to 0, is 0 so the partial derivative there is 0.

    The same is true for the partial derivative with respect to y at (0,0).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook