Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) [/itex]

[itex]= -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ} (\frac{∂L}{∂(∂_{μ}\phi)} δ(\phi)) [/itex]

How can we even extract anything within that delta? How does that even work? I feel like I'm missing some basic calculus here, but can't find anything in my textbooks or google.

(those "L"s are supposed to be Lagrangian densities, I just don't know the curly script for L in latex. all of this is inside an integral and there's another term, but neither of those change. I also posted to calculus but no one knew enough.)

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# Expanding delta in Field Theory Derivation of Euler-Lagrange Equations

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