If z is complex, the following rules are true, right?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d}{dz}z^n = nz^{n-1}[/tex]

[tex]\frac{d}{dz}\ln{g(z)} = \frac{1}{g(z)} \frac{d}{dz}g(z)[/tex]

[tex] \frac{d}{dz}e^{g(z)}=e^{g(z)}\frac{d}{dz}g(z)[/tex]

These are of course the same rules as for real variables.

When do I need to be careful about taking derivatives with respect to complex variables?

Do all of the same rules apply as with real variables? Or do some rules fail?

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# When derivates w/ resp to complex variables differ from real derivatives?

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