I was trying variate an action in General Relativity, and I come to the next calculus:
$\delta(g^{\alpha\beta}g^{\mu\nu})$
And I did:
$\delta(g^{\alpha\beta}g^{\mu\nu})=g^{\alpha\beta}\delta g^{\mu\nu}+g^{\mu\nu}\delta g^{\alpha\beta}$
I don´t know how to follow, what's the next step?
If $\delta=\partial/\partial g^{\mu\nu}$
The fist term would be just $g^{\alpha \beta}$? And what about the second term?
