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
a question about the derivate with respect to z , of a composition
0
$\begingroup$
complex-analysis
derivatives
-
1"I don't know what $g_w$ means" - it's the derivative of $g$ with respect to $w$. – 2012-08-07
-
0What is $g_\bar w$? – 2012-08-07
-
0In 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 stuck – 2012-08-07
-
0It 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