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I'm trying to understand the Maxwell's Equation example from David Tongs QFT notes. He uses the Lagrangian: $$ L = -\frac{1}{2}(\partial_{\mu}A_{\nu})(\partial^{\mu}A^{\nu})+\frac{1}{2}(\partial_{\mu}A^{\mu})^2 $$ To compute the equations of motion. I understand the Einstein summation notation but I don't understand how one computes $ \frac{\partial{L}}{\partial(\partial_{\mu}A_{\nu})}$

Can someone explain to me the steps to compute: $$ \frac{\partial{L}}{\partial(\partial_{\mu}A_{\nu})} = -\partial^{\mu}A^{\nu}+(\partial_{\rho}A^{\rho})\eta^{\mu\nu} $$


marked as duplicate by AccidentalFourierTransform, Thomas Fritsch, GiorgioP, Kyle Kanos, John Rennie electromagnetism Jun 20 at 16:05

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