I want Sinc' to return 0, but instead it returns Indeterminate.
Unprotect[Sinc] Unprotect[Derivative] Derivative[Sinc] ^= 0
But it doesn't work.
Maybe this needs to be similar to this (from the help files for Derivative)
f'[x_] := If[PossibleZeroQ[x], N[0, Precision[x]], (x Cos[x] - Sin[x])/x^2];