I do know the next result’s appropriate however I am questioning if how I am interested by it’s okay.

$f=frac{1}{2sigma^2}$

I decded to go together with $u=2sigma^2$ so $du = 1$

$f=frac{1}{u} implies frac{df}{du}=-frac{1}{u^2}du implies -frac{1}{4sigma^4}$

I am a bit confused becaues this thread talked about taking the spinoff w.r.t. $x^2$ however it appears to me that if I did it there approach I might have

$frac{df}{du}frac{du}{dsigma} = frac{1}{4sigma^4}4sigma=frac{1}{sigma^3}$. Which appears inaccurate.

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