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.

翻译：提出了一种用于快速求值多项式与有理Bézier曲线导数的新几何方法。该方法应用了作者近期提出的多项式与有理Bézier曲线求值算法。数值测试表明，该新方法比基于著名de Casteljau算法的方法具有更高的效率。即使对于高次有理Bézier曲线的高阶导数，该算法仍能良好运行。