I mentioned many times about differention of cinterp() , ainterp(). Here is one of the post http://en.smath.info/forum/default.aspx?g=posts&t=1803#post9550 . It is supposed that if we interpolate our data with splines, that quite a chance is that we want to differentiate and integrate the obtained spline function.
Therefore, I think that SMath must have quite reliable functions for strictly numerical differentioation and integration in its core functions.
Rregards, Radovan