I'm trying to prove this relation: $(\delta (f(x)))' = f'(x) \delta' (f(x)) $, where $f(x)$ is a monotone function. I just end up tangled in different derivatives of Dirac delta function or derivatives of $f(x)$ and I can't solve it. Can anyone help?
2026-03-26 17:47:31.1774547251
Derivative of Dirac delta of f(x)
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I figured it out, I just had to integrate both sides and then use substitution: $f(x) =t$ and then I got the same value on both sides of the equation. Thank you to everyone who tried to help me with this problem!