Derivative of metric tesor and its trace

[vaibhavtewari]

I would like to ask, how these identities are true

$$\partial_{\mu}(-g)=(-g)g^{\alpha\beta}\partial_{\mu}g_{\alpha\beta}$$

and

$$\partial_{\mu}g^{\alpha\beta}=-g^{\alpha\lambda}g^{\beta\rho}\partial_{\mu}g_{\lambda\rho}$$

Sorry I meant" derivative of metric tensor and its determinant", I was able to prove the second identity, please help me with the first one.

 

[Mentz114]

The first one is found using Jacobi's formula. See for instance

http://en.wikipedia.org/wiki/Jacobi's_formula

also

http://en.wikipedia.org/wiki/Einstein–Hilbert_action

 

[vaibhavtewari]

I apologize for late reply...the link you provided is very much helpful...thankyou very much for your help.