So i am studying GR at the moment, and I've been trying to figure out what the derivative (not covarient) of the mixed metric tensor $$\delta^\mu_\nu$$ would be, since this tensor is just the identity matrix surely its derivative should be zero. Yet at the same time $$\delta^\mu_\nu = g_{\alpha\nu}g^{\alpha\mu}$$ which means $$\partial_\beta \delta^\mu_\nu = g_{\alpha\nu}\partial_\beta g^{\alpha\mu} + g^{\alpha\mu}\partial_\beta g_{\alpha\nu}$$ so I cannot see why it would be equal to zero. Can anybody help me out?(adsbygoogle = window.adsbygoogle || []).push({});

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# Derivative of the mixed metric tensor

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