(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

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The attempt at a solution

I have been trying to understand how to obtain the R.H.S. of each property from its L.H.S. but i can't find how, although i know that it's somehow related to differentiating the L.H.S. I am having a hard time to prove these properties, starting with the first one.

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# Homework Help: Properties of the D operator

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