Trying to understand index notation in the context of spacetime. If I have $x^{\mu}$ and then set $\mu=\phi$ (for example), is it acceptable to then write $x^{\phi}$ or should I just write $\phi$ ? For example, can I write $$\frac{\partial g_{\mu\nu}}{\partial x^{\mu}}$$ as $$\frac{\partial g_{\phi\nu}}{\partial x^{\phi}},$$ or should I stick with$$\frac{\partial g_{\phi\nu}}{\partial\phi}?$$ Thanks.