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Non-analytic - Xorter - 04/04/2017

I am interested in how to get theĀ derivative of non-analytic functions.
For instance:
f(x) = 0 if x is reational and 0 otherwise.
f(x) = x xor 2x
f(x) = Y(1;x) (twist function of multidimensional "base units")
and so on...
How?