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I understand the following equation to be correct, but why can we treat the differentials as fractions and cancel them out? What would be the correct way to view it?

$$ \int_{-\pi/a} ^{\pi/a}dk_xf(k_x)\frac{d^2}{dk_x^2}[\delta(k_x)] = \int_{-\pi/a} ^{\pi/a}f(k_x)d \left(\frac{d}{dk_x} [\delta(k_x)] \right) $$

user91820
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  • If you define $dg(x):=\frac{dg}{dx}dx$, then the equality in the OP holds. The symbol $d$ refers to the operator called differential. My question is: what did you gain rewriting the integral like that? – Avitus Sep 26 '14 at 07:55
  • You may have a look here! I think you'll find answers to you question; anyway you'll find it useful: http://math.stackexchange.com/questions/21199/is-frac-textrmdy-textrmdx-not-a-ratio – nullgeppetto Sep 26 '14 at 07:55
  • To me, both sides of the equation are unintelligible. – Christian Blatter Sep 26 '14 at 08:23

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