I'm reading a solution to a problem that deals with solving a differential equation using the Fourier transform, and I can't follow one of the steps. In the Fourier domain we have: $$- {4 \over ({4 + \omega^2})^2} = -{1/2 \over 4 + \omega^2} + \frac{\partial}{\partial\omega} (-{1/2 \omega \over 4 + \omega^2})$$ I've done partial fractions, but I have never seen something being split up into two terms where one is a derivative. I would like to know which rules were used to establish this identity. It would also be nice to know where I can read more about these rules.
2026-03-27 16:47:43.1774630063
Splitting fraction in Fourier domain into two terms, where one is a derivative
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