# How to evaluate components of covariant derivative

+1 vote

I am stumbled how to define covariant derivative, so I can evaluate components of expresions such as:

-\nabla_{\alpha} p(r) = (\rho(r) + p(r))a_\alpha + u^\sigma \nabla_{\sigma} p(r) u_{\alpha}
where a_{\alpha} = u^\tau \nabla_{\tau} u_{\alpha}


presume I have define metric and expresion for Christofel symbols of 2nd kind in usual way.
Also how to make difference if nabla is acting on vector or covector?