I cannot find a derivative of remainder function (i.e. derivative of
a(x) mod b(x) with respect to
x is a real number and
b() is also real-valued functions) in tables of derivatives. Without the loss of generality, we may assume (and it desired at all), that continuous approximation is acceptable.
I note, that
(a(x) mod const)' ~ a'(x),
(c(x) mod c(x))' = 0, but still I can't conclude form of desired right hand side
(a(x) mod b(x))' -> ? function from these borderline cases (maybe dimensional method or method of indefinite coefficients in some form is applicable, but I have not an intuitions of how).
What is the generalized (in sense of continuity) form of remainder derivative?
I mean a remainder function as presented on x86/x86-64 architectures (FPREM and FPREM1).