If I have a partial derivative for $A_\mu$ of the form $$\frac{\partial A_\mu}{\partial(\partial_\mu A_\upsilon)}$$ where $\partial_\mu A_\upsilon = \frac{\partial A_\upsilon}{\partial x^\mu}$ is the derivative of $A_\upsilon$ with respect to the spacetime coordinates, how do I go about evaluating this expression? In Sean Carroll's Intro to GR, he gets terms like these in equations that he seems to just discard, so I suspect the answer is $0$, but I don't know the specifics of how that results from the derivative above.
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