  New geometric methods for fast evaluation of derivatives of polynomial and
rational B\'{e}zier curves are proposed. They apply an algorithm for evaluating
polynomial or rational B\'{e}zier curves, which was recently given by the
authors. Numerical tests show that the new approach is more efficient than the
methods which use the famous de Casteljau algorithm. The algorithms work well
even for high-order derivatives of rational B\'{e}zier curves of high degrees.
