substitution in differentiation



Hi everybody,

I've got a function u depending on a variable x.  So I declared:

(%i1)      depends(u,x);
 
I now want to differentiate u with respect to x.  So:

(%i2)      diff(u,x);

Now I want to substitute the independent variable x with l*X,  where  l 
is  a constant parameter.  What I want to obtain is:

d u        1    d u
------   = ---   -------
d x         l     d X


With subst(l*X,x,diff(u,x)) or ratsubst(l*X,x,diff(u,x)) , I get:

d u         d u
------   = ------------
d x         d (l*X)


Any Ideas???  expand does not work.

I have the same problem with the function u, when I want to substitute u 
with l*U. Here l is constant, U is function of x. What I want to get is:

d u              d U
------   =  l   ---------
d x               d x

With subst(l*X,x,diff(u,x)) or ratsubst(l*X,x,diff(u,x)) , I get:

d u         d (l*U)
------   = ------------
d x         d x


Again expand does not help.


Many thanks in advance.

Marc Hodapp