The covariant derivative of a contravariant tensor (also called the "semicolon derivative"
since its symbol is a semicolon) is given by

(1)

(2)

(Weinberg 1972, p. 103), where is a Christoffel
symbol, Einstein summation has been used
in the last term, and is a comma derivative.
The notation ,
which is a generalization of the symbol commonly used to denote the divergence
of a vector function in three dimensions, is sometimes also used.