Radon–Nikodym derivative and “normal” derivative

The Radon–Nikodym theorem states that,

given a measurable space $(X,\Sigma)$, if a $\sigma$-finite measure $\nu$ on $(X,\Sigma)$ is absolutely continuous with respect to a $\sigma$-finite measure $\mu$ on $(X,\Sigma)$, then there is a measurable function $f$ on $X$ and taking values in $[0,\infty)$, such that

$$\nu(A) = \int_A f \, d\mu$$

for any measurable set $A$.

$f$ is called the Radon–Nikodym derivative of $\nu$ wrt $\mu$.

I was wondering in what cases the concept of Radon–Nikodym derivative and the concept of derivative in real analysis can coincide and how?

Thanks and regards!

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