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if I have a function [tex]f:\mathbb{R}\rightarrow \mathbb{C}[/tex], what are the conditions onffor which the derivative of the Logarithm exist?

[tex]\frac{d}{dx}\mathrm{Log} (f(x))[/tex] exists?

Note that here I defined:

[tex]Log(z)=\log |z| + Arg(z)[/tex], where [itex]-\pi< Arg(z) \leq \pi[/itex]

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# When does derivative of complex Log exist?

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