Inthispaperthederivativeanditsexceptionalsetaccordingtothealternativelyjumpingfunctionandself-similarfunctionrespectivelyarediscussed.Andintheappendix,aproofofthestatement1.2(2)of“CalculusonCantortriadicset(Ⅱ)—derivative”whichisimportanttothediscussionofexceptionalsetisgiven.