I have a question about the z-transform: In the (Oppenheim's Signals and Systems) book it is written: If the z-transform of x[n] is X(z) with ROC=R, then the z-transform of nx[n] is -zdX(z)/dz with the same ROC. I don't understand why the ROC remains unchanged. Some books say "it follows from the fact that X(z) is analytic", some other books say "note that Laurent z-transform is differentiable within the ROC". But these reasons are not clear to me at all! Any help will be appreciated.