I am running into issues trying to find the derivation of f(z) below. Please help
Technically the word is "differentiation", not "derivation".
I presume you know that if f(z)= f(x+ iy)= u(x, y)+ iv(x,y) then
(The fact that those two expressions on the right are equal is the "Cauchy- Rieman" equations. You can use either one.)
Here, of course, you have