When you study physics, you never really delve into the reasons behind some of mathematical identities, i was curious about this one as it occurs in Bloch's Theorem (correct me if I go wrong):(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d}{dt}(\frac{dE}{dk})=\frac{d^{2}E}{dtdk}=\frac{d^{2}E}{dkdt}=(\frac{d^{2}E}{dk^{2}})\frac{dk}{dt}[/tex]

I checked this and the first and last part are equivalent.

Does that mean you can interchange the numerators and denominators freely? (given that the derivative is an operator)

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# Derivative identity

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