I have the function f(x)= x+1 for x greater or equal to 0 and -x-1 for x less than 0 ,

I have to prove that f has no weak derivative.

I computed <Df,g>= 2g(0)+\int_0^\infty g(x)dx - \int_{-\infty}^0 g(x)dx , where g is a test function. But how do I prove that this is of the form \int_{-infty}^\infty h(x)g(x)dx and that Df is not in L^1_{loc}(R)?

Thanks.