Reducing the number of multiplications for the evaluation of a polynomial and its derivatives does not necessarily mean that one should expect a commensurate reduction of the total cost of computation. In this paper we present a cost analysis for a family of algorithms, which computes all derivatives of a polynomial in 3n−2 multiplications or divisions. This represents an improvement over the classical methods, which require 1/2n(n+1) multiplications. The analysis, however, reveals the presence of a multiplications-divisions cost trade-off due to which the cost complexity remainsO(ξ2n3) for all algorithms irrespective of any reduction in the number of arithmetic operations.