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I know that the derivative of Dirac-delta function (##\delta'(x-x') = \frac{d}{dx} (\delta(x-x')))## does the following:

##\int_{-\infty}^{\infty}\psi(x')*\delta'(x-x') dx' = \frac{d\psi(x)}{dx}##

it is easy to visualize how the delta function and the function ##\psi(x')## interact along the x' axis to give the derivative with respect to x ( i.e scaling ##\psi(x\pm \varepsilon ) ## at each bump ##\pm \varepsilon ##..etc)

However, I am stuck at a situation where

##\int_{-\infty}^{\infty}\psi(x')*\delta'(x-x') dx ##

I am not sure what to do here. But what I think it should equal to is ##\frac{-d\psi(x')}{dx'}## just by applying the same way of thinking as when the integration variable is the same as that of of the function ##\psi##. But here the function I think acts as constant in this integral which makes me doubt my answer. Is this answer correct?

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# I Dirac-Delta Function, Different Integration Variable

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