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Partial differential problem

  1. Jul 7, 2012 #1
    I have calculated 3 times and I still don't get the answer. The answer should be 0.
    Here's the question and my work. Which part am I wrong?


    f(x,y) = 1/√(1-2xy+y^2)

    Prove that ∂/∂x{(1-x^2)*∂f/∂x} + ∂/∂y{(y^2)*∂f/∂y} = 0
     

    Attached Files:

  2. jcsd
  3. Jul 7, 2012 #2

    haruspex

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    The powers "-1/2" in the very first step for both fx and fy should be "+1/2".
     
  4. Jul 8, 2012 #3
    I think my first partial derivative is correct.

    because the power of the original function is +1/2 so when we differentiate it,it becomes
    1/2 - 1 = -1/2

    But I don't get 0 for the final answer
     
  5. Jul 8, 2012 #4

    haruspex

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    Sorry, you're right. The mistakes are in the last line.
    In fact, hardly any of the last line looks right to me!
    E.g. the first term should be (writing g = 1/f):
    [-2xyg3 + 3y2(1-x2)g]/g6
    No?
     
  6. Jul 8, 2012 #5
    Yeah, I know what went wrong now :D I used the quotient rule incorrectly.
    Thanks, I have solved this!!! :)
     
    Last edited: Jul 8, 2012
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