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In page 62 of Shankar's Principles of Quantum Mechanics, the author conveys the following: $$\int \delta'( x-x') f(x') dx' = \int \frac{d\delta(x-x')}{dx}f(x')dx'= \frac{d}{dx} \int \delta(x-x') f(x') dx'= \frac{d}{dx}f(x)$$

Where $\delta(x-x')$ is the Dirac-Delta function. Under what conditions can one shift the derivative outside the integral?

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closed as off-topic by By Symmetry, ACuriousMind Jun 7 '18 at 17:10

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  • $\begingroup$ en.wikipedia.org/wiki/… Although distributions in place of functions make this a little more complicated. With dirac-delta functions, you can also get the same result via integrating by parts. $\endgroup$ – Jahan Claes Jun 7 '18 at 16:21