# How to prove matrix identities involving the determinant, logarithm and derivatives

I'm talking about these specific relations, where g is the determinant of the metric tensor (so it's symmetric spscific), which is a function of $x^k$:

$\frac{1}{2g}\frac{\partial g}{\partial x^k}=\frac{1}{2}\frac{\partial \ln g}{\partial x^k}$

I've tried making discrete variations of the matrix, but I can't reach this particular relation.

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