This is from a book by Srednicki:
I can't make sense of the third equality. I suppose that $x^\mu$ is the projection operator. How can it be that $[\partial^\rho,x^\mu]=g^{\rho\mu}$? I know that $g^{\mu\nu}=\partial^\rho\cdot\partial^\mu$, but this does not lead me anywhere. I think that my confusion arises from not knowing exactly what $x^\mu$ is.