I am doing work with variables $x_1$, $x_2$, $x_3$, etc. In the process I generate polynomials which are of the form $$ p = x_1 x_2 x_3 + x_2^2 x_3 + x_1^2 x_2 + \ldots $$ I would like to be able to do operations on each of these monomials as if they were independent variables.

So suppose one has a list of monomials, $$ \{x_1^2 x_2, x_3 x_2 x_1, x_1^2 x_3, \ldots\} $$ Is there a way of changing the attributes of the elements in this list so that one can treat these monomials as single variables? For example, this would allow one to differentiate with respect to a specific monomial, as opposed to a single $x_i$.

I realize this may not be possible in Mathematica but it would greatly simplify my work if this could be done. Thanks for any advice.