Variation of inverse metric
= Variation of inverse metric
{title2=$\delta g^{ab}=-g^{ac}g^{bd}\delta g_{cd}$}
Differentiating $g^{ac}g_{cb}=\delta^a_b$ and multiplying by the inverse gives the displayed <variation>. It is the <matrix inverse> <derivative>, expressed with the covariant and contravariant components of a <metric tensor>.