Functional Derivative: Evaluating & Understanding

[aaaa202]

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.

 

[thierrykauf]

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