Some notes on the inversion of confluent Vandermonde matrices

The determination of the inverse of the confluent Vandermonde matrix stood often in the focus of attention. To achieve this aim many methods were elaborated. Based on the Leibniz rule of derivation, in this correspondence the elements of the inverse confluent Vandermonde matrix are computed, and, at the same time, a common explanation is given for the various methods seeming at the first sight quite different.