  It is possible to perform some operations with extrafunctions applying these
operations separately to each coordinate. Operations performed in this manner
are called regular. It is proved that it is possible to extend several
operations with functions to regular operations with extrafunctions. Examples
of such operations are addition of real functions and multiplication of real
functions by numbers. However, there are operations with functions the
extension of which by coordinates does not work because their application is
not invariant with respect to representations of extrafunctions. One of such
operations is differentiation, which is important for calculus, differential
equations and many applications. In this work, a method of regularization of
irregular operations is developed and applied to differentiation. The main
constructions are put together in the context of fiber bundles over hyperspaces
of differential vector spaces and differential algebras.
