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Another question thrown at you

  1. Sep 21, 2006 #1
    I think I'll get banned soon posting multiple questions at the same time, but allow me to continue,
    if f,g:R-->R both of class C2(differentiable twice)
    Define F(x,y)=f(x+g(y))
    Show that (DxF)(DxDyF)=(DyF)(D^2xF) where D^2xF is second order partial derivative with respect to x
    I'm dying here...
  2. jcsd
  3. Sep 21, 2006 #2
    umm... forget it I think I can do this one.. lol
  4. Sep 21, 2006 #3
    Umm... I'm stuck..
  5. Sep 21, 2006 #4
    Rewrite [itex]F_x(x,y)[/itex] and [itex]F_{yx}(x,y)[/itex] in terms of derivatives of [itex]f(x+g(y))[/itex] and [itex]g(y)[/itex] (the rest is straightforward manipulation, using the chain rule).
  6. Sep 21, 2006 #5
    Yes!!! It did work!! Thank you!
    Now please the remaining questions I posted, could anyone please answer??
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