Polynomial approximation is a classical problem, for which the monomial basis leads to the notoriously ill-conditioned Vandermonde matrix. Recently, Brubeck et al advocated to resolve the issue by change of basis on the fly. In this talk, we extend the idea to dealing with the confluent Vandermonde matrix, which enables us to compute the derivatives of high degree polynomials to high precision. It also makes many applications involving derivatives possible, to be illustrated by numerical examples.