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According to page 7 of the PDF document

$$ \frac{\delta}{\delta f} \int \left( \frac{df^2 }{d^2 x} \right)^2 dx = \int \frac{df^4}{d^4 x} dx $$

I would like help proving this statement.

Although I can show that

$$ \int \left( \frac{df^2 }{d^2 x} \right)^2 dx = \int \frac{df^4}{d^4 x} f dx $$

My attempts at "constructing" the functional derivative of this expression isn't dropping the term $f$. I'm not even sure this is the right way to go about solving the problem.

2 Answers 2