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offscene

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- Homework Statement
- Given ##\mathcal{L} = -\frac{1}{2}(\partial_\mu \mathcal{A}_\nu)(\partial^\mu \mathcal{A}^\nu)+\frac{1}{2}(\partial_\mu \mathcal{A}^\mu)^2##, compute ##\frac{\partial{\mathcal{L}}}{\partial(\partial_\mu \mathcal{A}_\nu)}##.

- Relevant Equations
- Euler-Lagrange equations of motion.

This isn't a homework problem (it's an example from David Tong's QFT notes where I didn't understand the steps he took), but I am confused as to how exactly to take the partial derivative of the Lagrangian with respect to ##\partial(\partial_\mu \mathcal{A}_\nu)##. (Note the answer is: ##-\partial^\mu \mathcal{A}^\nu+(\partial_\rho \mathcal{A}^\rho)\eta^{\mu \nu}##)

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