When we write the components of the total covariant derivative , it is common practice to use semicolon to separate indices resulting from differentiation of a tensor field.

For example, the components of the total covariant derivative of a vector field \(Y=Y^iE_i\), which is a \((1,1)\)-tensor, are given by

\begin{equation*} \nabla Y={Y^i}_{;j}\,E_i\otimes \varepsilon^j \end{equation*}

with

\begin{equation*} {Y^i}_{;j}=E_jY^i+Y^k\Gamma^i_{jk}. \end{equation*}