Functional Derivative: Evaluating & Understanding

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To evaluate a functional derivative involving an exponential, it's essential to understand the context of quantum field theory (QFT) and related concepts like path integrals and Schwinger sources. Standard methods for taking functional derivatives often involve polynomials, but the principles can be adapted for exponential forms. Resources on QFT can provide valuable insights into handling such derivatives effectively. Exploring academic papers or textbooks focused on functional analysis and QFT may yield clearer explanations. Understanding these concepts is crucial for accurately evaluating the functional derivative in question.
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In my textbook (see attached picture) there appears a functional derivative, but I honestly don't know how to evaluate a quantity like this. What should I do? I have tried to google but all I could find was how to take functional derivatives, where polynomials appeared under the integral, while here is an exponential.
 

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You need to google path integrals, Schwinger sources, this is all standard QFT
 

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