A distribution $u=\frac{1}{x}$

Question

I am interested in finding a distribution $u \in \mathcal{D}'(\mathbb{R})$ such that

$u=0$ on $(-\infty,0)$ and $u=\frac{1}{x}$ on $(0,\infty)$.

This is exercise 1.4 in Friedlander. Hints or help is welcome! Thanks.

Answer 1

Hint:

$\log|x|$ is locally integrable and $(\log|x|)'=1/x$.