# Derivative of Complex Function

• January 28th 2010, 01:06 PM
paupsers
Derivative of Complex Function
Determine where f'(z) exists and find its value when
$f(z)=x^2+iy^2$

My book gives NO explanation of how to find derivatives when the function f(z) isn't given in terms of z, as it is here. How do you solve these?
• January 28th 2010, 02:49 PM
shawsend
Hi. But $x=\frac{z+\overline{z}}{2}$ and $y=\frac{z-\overline{z}}{2i}$ right? How about just using the chain rule then to compute $\frac{\partial f}{\partial z}$?
• January 28th 2010, 03:05 PM
Plato
Quote:

Originally Posted by paupsers
Determine where f'(z) exists and find its value when $f(z)=x^2+iy^2$

Here is the link you need.