  The smooth function reconstruction needs to use derivatives. In 2010, we used
the gradually varied derivatives to successfully constructed smooth surfaces
for real data. We also briefly explained why the gradually varied derivatives
are needed. In the this paper, we present more reasons to enlighten of forcing
derivatives to be continuous is necessary. This requirement seems not a must in
theory for functions in continuous space, but it is truly important in function
reconstruction for real problems. This paper is also to extend the meaning of
the methodology for gradually varied derivatives to general purposes by
considering forcing calculated derivatives to be "continuous" or gradually
varied.
