Fμν ∂Fσμ/∂xν = -½ Fμν ∂Fμν/∂xσ
= -½ gμα gνβ Fαβ ∂Fμν/∂xσ.
Owing to symmetry, this expression can also be written in the form
= -1/4 [gμα gνβ Fαβ ∂Fμν/∂xσ
+ gμα gνβ ∂Fαβ/∂xσ Fμν],
which can also be put in the form
- 1/4 ∂/∂xσ (gμα gνβ Fαβ Fμν)
+ 1/4 Fαβ Fμν ∂/∂xσ (gμα gνβ).
The first of these terms can be written shortly as
- 1/4 ∂/∂xσ (Fμν Fμν),