From the use of the Minkowski metric, converting between contravariant and covariant
[math]\displaystyle{ \mathbf x_{\mu} \equiv \eta_{\mu}^{\mu} \mathbf x^{\mu} }[/math]
[math]\displaystyle{ \nabla_{\mu}=\partial_{\mu} }[/math]
[math]\displaystyle{ \mathbf \partial_\mu \equiv \Biggl [ \frac{\partial}{\partial t}\quad \frac{\partial}{\partial x}\quad \frac{\partial}{\partial y}\quad \frac{\partial}{\partial z}\Biggr ]=\Biggl [\frac{\partial}{\partial x^0}\quad \frac{\partial}{\partial x^1}\quad \frac{\partial}{\partial x^2}\quad \frac{\partial}{\partial x^3}\Biggr ] }[/math]