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How come differentiation of a unit step function is Dirac Delta? Can anybody give me a concrete mathematical proof? I only found some intuitive kind of explanation, that at $t = 0$, slope of $u(t)$ increases rapidly, thus derivative at $t = 0$ becomes a Dirac Delta Function. Please give a concrete mathematical proof. Thanks.

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marked as duplicate by user147263, Alex M., Leucippus, user91500, SchrodingersCat Nov 27 '15 at 6:04

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ For rigor, you need to know about the theory of distributions. In standard calculus, this derivative just doesn't exist. $\endgroup$ – Yves Daoust Nov 26 '15 at 20:01
  • $\begingroup$ @AlexM. Good point. I edited the title of the latter question to make it better searchable, and voted to close the former as a duplicate of it. $\endgroup$ – user147263 Nov 26 '15 at 20:14