content_image/313379.jpg content_image/313378.jpg content_image/313377.jpg
Now we must prove that g $^{αβ}$∂$_{µ}$ g$_{αβ}$ is equal to this last quantity: 

<img src='content_image/313379.jpg'>

## Use of Identity 

We will use an important example of the identity Eq. (F.1): 

<img src='content_image/313378.jpg'>

The last equality comes from taking the variation of g$_{µν}$g µν = δ ν ν = #: 

<img src='content_image/313377.jpg'>

