Results 1 to 2 of 2

Math Help - Theorem concerning partial differentiation

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    2

    Theorem concerning partial differentiation

    The question is:

    Prove that
    f(x,y) = xy / (x^2+y^2)^2 x,y are not zero
    f(0,0) = 0

    satisfies Laplace's equation d^2f/dx^2 + d^2f/dy^2 = 0 everywhere

    And we are supposed to use the theorem which states that the function f is differentiable at (a,b) if f and its partials exist at each point of the neighborhood and continuous at (a,b)

    No idea how to start this problem....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,392
    Thanks
    55
    Quote Originally Posted by geegee View Post
    The question is:

    Prove that
    f(x,y) = xy / (x^2+y^2)^2 x,y are not zero
    f(0,0) = 0

    satisfies Laplace's equation d^2f/dx^2 + d^2f/dy^2 = 0 everywhere

    And we are supposed to use the theorem which states that the function f is differentiable at (a,b) if f and its partials exist at each point of the neighborhood and continuous at (a,b)

    No idea how to start this problem....
    Calculate \frac{\partial^2 f}{\partial x^2} and \frac{\partial^2 f}{\partial y^2} show that when you add them you get 0. It's really straight forward.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Partial differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 2nd 2011, 03:58 PM
  2. Replies: 2
    Last Post: July 26th 2010, 06:24 PM
  3. A partial differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 21st 2010, 06:51 AM
  4. partial differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 27th 2009, 07:18 PM
  5. Partial Differentiation 2
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 20th 2007, 03:54 AM

Search Tags


/mathhelpforum @mathhelpforum