Math homework help

[KillerCharlie]

Is there anyone here familiar with complex differentiation and holomorphic (analytic) functions? If so, I have a problem I'll post that I'm not understanding.

 

[bigal40]

maybe try www.cramster.com go to the answer board section

 

[eLiu]

? If it's analytic, you can differentiate in any direction you want... so if it's f(z), just do df/dz as if nothing is special.

 

[KillerCharlie]

Find the derivative f'(z), where it exists, and state where f is analytic.
f=(x+y) + i(sin x + cos y)

I really don't understand this well. I use the Cauchy-Riemann relations and get

ux=1, uy=-sin(y)
uv=1 vx=-cos(x)

These are equal at y=-pi/2+2kpi and x=-pi+2kpi
They also seem to be continuous...

So from here I'm not sure how go get f' and I'm not sure where it's analytic.