Infinitesimal Perturbation Analysis (IPA) is perhaps the most efficient derivative estimation method for many practical discrete-event stochastic systems, whenever it applies. But there are many situations where it does not apply directly. Alternative methods such as Likelihood Ratios (LR), Finite Perturbation Analysis (FPA), Smoothed Perturbation Analysis (SPA), Rare Perturbation Analysis (RPA), and a few others, have been proposed and could be used when IPA does not apply directly. In this paper, we discuss some links that exist between these methods and explain them by showing how each of them can be applied to a specific example, namely to estimate the derivative of the expected number of customers per regenerative cycle in a GI/G/1 queue, with respect to parameters of the interarrival and/or service-time distributions. We also give the results of numerical experiments to compare the performances of these methods.