KummerU(p, q, t) is (by definition) a solution of the ODE t y'' + (q - t) y' - p y = 0. The corresponding KummerM is the other solution. The independent variable of the ODE is t, so it's relatively easy to differentiate the solution, y, with respect to t.
I said earlier that Maple didn't know how to differentiate it with respect to p. That's not 100% true. If you do FunctionAdvisor(KummerU(p,q,t)) and expand the section "differentiation rule", you'll see that there's a fantastically complicated formula of an infinite series of improper integrals and GAMMA functions given as the derivative with respect to the first parameter.
Do you have some reason to want the series with respect to p, or is it just curiosity?