Derivatives of the radicals of moduli

The radicals of moduli are investigated as functors. Particular attention is given over to the derivatives of the functor of a radical. The function $R^0r$ turns out to be a hereditary radical containing the given one. Several relations between the $R^ir$ are proved. The article is concluded with a description of the hereditary radicals of a Prüfer ring. All the radicals of a Prüfer ring have the form of torsions in an integral domain.