Consider the function $$H(\alpha) = \int_{\Omega(\alpha)} h(\alpha,x) dx,$$ where $\alpha\in\mathbb{R}$ and $\Omega(\alpha)\subset\mathbb{R}^2$ is a domain that varies continuously with $\alpha$. Is there a way to write $\frac{\partial H}{\partial\alpha}$?
2026-04-25 10:00:47.1777111247
Derivative of an integral over a varying domain
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Yes, you should look at this pdf, chapter A.2.