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## Main Question or Discussion Point

In curved space, can I raise an index on a tensor that is being differentiated? Ie, is the following true?

[tex]g^{\mu\lambda}\partial^\nu(F_{\mu\nu})=\partial^\nu(F^\lambda_\nu)[/tex]

[tex]g^{\mu\lambda}\partial^\nu(F_{\mu\nu})=\partial^\nu(F^\lambda_\nu)[/tex]