Another question thrown at you

1. Sep 21, 2006

precondition

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. Sep 21, 2006

precondition

umm... forget it I think I can do this one.. lol

3. Sep 21, 2006

precondition

Umm... I'm stuck..

4. Sep 21, 2006

Data

Rewrite $F_x(x,y)$ and $F_{yx}(x,y)$ in terms of derivatives of $f(x+g(y))$ and $g(y)$ (the rest is straightforward manipulation, using the chain rule).

5. Sep 21, 2006

precondition

Yes!!! It did work!! Thank you!