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for the Lagrangian density $$\mathscr{L}=\frac{1}{2}(\partial_{\mu}A^{\mu})^2$$

how can I get this $$\frac{\partial{\mathscr{L}}}{\partial(\partial_{\mu}A_\nu)}=(\partial_\rho A^\rho)\eta^{\mu\nu}$$

or I can only get $\frac{\partial{\mathscr{L}}}{\partial(\partial_{\mu}A_\nu)}=\partial_\rho A^\rho$ but where the $\eta^{\mu\nu}$ comes from.

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Writing $$\mathscr{L}=\frac{1}{2}(\partial_{\mu}A^{\mu})^2=\frac{1}{2}(\partial_{\mu}A_{\nu}\eta^{\mu\nu})^2$$ we can write $$\frac{\partial{\mathscr{L}}}{\partial(\partial_{\mu}A_\nu)}=\frac{1}{2}2(\partial_{\rho}A_{\sigma}\eta^{\rho\sigma})\eta^{\mu\nu}=(\partial_{\rho}A^{\rho})\eta^{\mu\nu} .$$

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