Partial Derivatives

Discussion in 'Math' started by Malsch, Dec 15, 2012.

  1. Malsch

    Thread Starter New Member

    Mar 19, 2011
    23
    0
    Hi, I have a function f(x,y). u = ax + by and v = bx - ay. a and b are constants. i need to prove that d2f/du2 + d2f/dv2 = 0.

    I have started out by finding df/du using chain rule:

    df/du = df/dx * dx/du + df/dy * dy/du

    Hence, df/du = df/a*dx + df/b*dy

    My problem is that now i need to find d^2f/du^2 but i do not know how to continue from df/du (ie. i do not know how i can differentiate df/a*dx + df/b*dy with respect to u).

    Thanks for reading
     
    Last edited: Dec 16, 2012
  2. Papabravo

    Expert

    Feb 24, 2006
    10,178
    1,799
    There is something missing. I can see how u and v are functions of x and y, BUT how is f(x,y) connected to u and v?

    So in order to answer the question you need to show three explicit functional relationships and you have only shown two.

    Second, be careful with your notation:
    df/a*dx + df/b*dy​
    is a meaningless construct. You can't mix the differential operator like an ordinary algebraic symbol.
     
  3. Malsch

    Thread Starter New Member

    Mar 19, 2011
    23
    0
    i miswrote what i need to prove and have edited it. i actually need to prove that d2f/du2 + d2f/dv2 = 0.
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,178
    1,799
    You still haven't established that f(x,y) has ANY dependence on u and v. As near as I can tell you haven't done squat to your original post.
     
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