3
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So I have no idea when it is allowed to do this:

$$x,y\in \mathbb{R}^{n} \ and \ f(x,y)\rightarrow \mathbb{R} \\ \frac{\partial }{\partial x_{k}}\int f(x,y)\ dy = \int \frac{\partial }{\partial x_{k}}f(x,y)\ dy \ k\in{{1,...,n}}$$

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