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I have the following integral

$$\int_a^b f(w, t)dt$$

where $w \in \Bbb R^n$ and I need to compute partial derivatives with respect to all components of $w$. How can I apply Leibniz rule to this problem?

Suggested answer:

$$\int_a^b \frac {\partial f(w, t)} {\partial w_i}dt$$ for all $i=1,\ldots,n$.

Rodrigo de Azevedo
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burer
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    This is not the Leibniz rule. It's just plain old differentiation under the integral sign. With appropriate hypotheses, just do the obvious thing. – Ted Shifrin Nov 17 '19 at 18:12
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    @Ted so, I can just put partial derivative under the integral? I edited answer, did I understand correctly? – burer Nov 17 '19 at 18:56
  • Yes, that's right (assuming the partial derivative is, say, continuous). I would write $\partial$ instead of $\delta$, of course. :) – Ted Shifrin Nov 17 '19 at 18:58
  • @Ted thanks for your help! – burer Nov 17 '19 at 20:29

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The answer is to use partial derivative under the integral for all needed component of w: $\int_a^b \frac {\partial f(w, t)} {\partial w_i}dt$ . And we don't need Leibniz rule, since the interval is constant

burer
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