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This is a problem from a book that I'm using to study complex analysis. I'm a little insecure with what I have to prove here, because, I don't know what it means $g_w$ for example . I'm a little confused... sorry for asking this stupid things

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    "I don't know what $g_w$ means" - it's the derivative of $g$ with respect to $w$.2012-08-07
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    What is $g_\bar w$?2012-08-07
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    In a try to prove it, i'll express all the derivates with respect to $z, \overline z $ in terms of derivates with respect to $x,y$ but I don't know how to proceed with the $" w , \overline w$ I'm very very stuck2012-08-07
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    It seems to me we should be reading $g_w,g_{\bar{w}}$ as the derivative of $g$ AT $w=f(z), \bar{w}=\bar{f(z)}$, by analogy with the real chain rule, rather than "with respect to" those variables.2012-08-07

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