Hi, I wonder if anyone knows when (maybe always?) it is true that, where(adsbygoogle = window.adsbygoogle || []).push({});

[itex]z=x+iy \text{ and } f : \mathbb{C} \to \mathbb{C} \text{ is expressed as } f=u+iv, \text{ that }

f'(z)=\frac{\partial u}{\partial x}+i\frac{\partial v}{\partial x}?

[/itex]

I'm pretty sure that this is true for [itex]f=exp.[/itex]

I should be able to find this but searching google for mathematics is a nightmare.

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# Derivative of a complex function in terms of real and imaginary parts.

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