# Tensor Notation - David Tongs Notes [duplicate]

This question already has an answer here:

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 StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 20 at 16:05

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.