I have taken sequential partial derivatives of a two variable polynomial fraction, resulting in a very long series of polynomials of form:

Cx^iy^j/(some product series of (1-x^k*y)^n)

What I wish to do is a series of basic truncations. First, I eliminate all polynomials that have x^i*y^j with i or j > 4 in the numerator. I keep looking over the documentation and stackexchange and cannot find anything that works for me. I'm also new to Mathematica.

Let me know how you'd do it.

Appreciate the answers, A