# Differential under an integral sign.

binbagsss
Sorry I'm not sure how you get math script on here, so have had to attach it.

It is a differential under an integral sign and I'm not too sure how to approach it.
Would you use Leibniz rule?
Do you differentiate or integrate first?
- where y is a function of x, and R of y

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• intediff.png
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No! What's asked for is the functional derivative. You get it by evaluating, how the integral changes when the function $y(x)$ changes by an infinitesimal $\delta y(x)$. Unfortunately the problem is not completely stated. You also need boundary conditions. If it's a usual variational problem like in Hamilton's principle, the values at the end points are fixed.