It discusses the derivative of absolute value functions with one variable.Firstly,a general conclusion is promoted,that is,the function f（x）=｜x｜ does not exist derivation at x=0,but if α0,f（x）=xα｜x｜ exists derivation at x=0,and we get an another conclusion.Then it discusses the derivative of function ｜f（x）｜ at x=x0 if f（x） gets derivation there.In the end of this paper,two examples are showed.