In this paper we prove that all high order non-biased spatial intensity derivative operators in images can be computed using linear combinations of separable filters. The separable filters are the same as those used by Haralick (1984), but different linear combinations are taken. A comparison of the number of operations necessary to compute the derivatives using separable and non-separable filters is made. The conclusion of our analysis is that the optimal way to compute the needed derivatives depends on which derivatives we have to compute, on the size of the window and on the order of expansion. Finally, we discuss the performance of an edge detector using these derivatives for unsmoothed and smoothed step edges.