integration and differentiation of f(g(x,y))

Hello,

I have some problems in generalizing my program.

A hopefully not too simplified example:
The problem is that for input functions like e.g. f(g(x,y)) I would like to use depends(g,[x,y]) and depends(f,g) so that the following differentiation uses the chain rule:
A : diff(g,x)/diff(g,y);
B : diff(f,y)/diff(f,x);
C : A*B;

and yields C=1 (can I get this result without using depends?)

However, I would like to be able to integrate this result as well, for instance: 
integrate(A*B*g,x)

integrate does not see the dependencies of g, resulting in the answer gx instead of keeping the integral over g(x,y)

The only option I see right now is: 
-always declare dependencies with depends
-when integration is needed, call my own integration routine and
  --temporarily remove the dependencies in depends
  --substitute the dependencies explicitly.
  --after the integration, create the dependencies again so that differentiation+chain rule work.

Is there another way? This approach seems a bit clumsy. I am open to suggestions.

A question: is there a reason that integrate does not recognize dependencies? Is it an option to make it recognize dependencies? Or is there a package that I missed that already does this?
Maybe a package that simplifies expressions and also recognizes the chain rule?

Regards,
Nijso
 
 		 	   		  
_________________________________________________________________
New Windows 7: Simplify what you do everyday. Find the right PC for you.
http://windows.microsoft.com/shop