T. Dent, K. Kearnes and A. Szendrei de ne the derivative, 0, of a
set of equations and show, for idempotent , that implies congruence modularity
if 0 is inconsistent ( 0 j= x y). In this paper we investigate other types of
derivatives that give similar results for congruence n-permutable for some n, and for
congruence semidistributivity.