How can I figure out ##\partial_\mu x^2## on the manifold ##(M,g)##? I thought that it should be ##2x_\mu##, but I think I'm wrong and the answer is ##2x_\mu+x^\nu x^\lambda \partial_\mu g_{\nu\lambda}##, right?! In particular, it seems to me, we can't write ##\partial_\mu=g_{\mu\nu}\partial^{\nu}##. However, we can raise or lower the indices of the covariant derivative with metric, I mean ##\nabla^\mu=g^{\mu\nu}\nabla_\nu##. Is this true because partial derivative is not a tensor but covariant derivative is? Could you please explain it to me?(adsbygoogle = window.adsbygoogle || []).push({});

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# Partial derivative of ##x^2##

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