Another question thrown at you

[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...

 

[precondition]

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

 

[precondition]

Umm... I'm stuck..

 

[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).

 

[precondition]

Yes! It did work! Thank you!
Now please the remaining questions I posted, could anyone please answer??