passing functions as argument one more time

Amli,

To elaborate a bit on RJF's discussion of functions vs. expressions....  The
point is not that the choice of functions vs. expressions is a matter of
taste or popularity; it is that Maxima supports manipulating expressions
very well, and functions not very well.  In Maxima, defined functions like
qq(aa):=... are very useful for operations on expressions, but not very
useful for manipulating mathematical functions.

Your script basically does two things: it takes derivatives of expressions
with respect to a variable; and it changes variables (e.g. from t to x).
The first can be done with diff( <expr>, <variable> ), the second with
subst( <newvar>, <oldvar>, <expr> ).

Also, there are some things in your script I don't understand.  You write

          g(f,x):=block([h:f],diff(h(x),x))$

What is the intent of the block([h:f]...)?  This has precisely the same
effect as diff(f(x),x) or (just to write it so the intent is a bit clearer)
diff( (f)(x),x).

                 -s