I am trying to compute the following partial derivative: $$ \frac{\partial}{\partial x}\iint_{\Omega(x)} f(x,\mathbf{w})d\mathbf{w} $$ with $f:\mathbb{R}\times \mathbb{R}^2\to \mathbb{R}$. In this article: Leibnitz Integral rule, the extension to high dimensional cases is only formulated for vector fields on time-variant surfaces, and I'm not sure how to translate that formulation for my case. How can I do that?
2026-02-24 08:15:58.1771920958
Leibnitz integral rule on double integral
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