Hi just a few questions on understanding the Cauchy-Riemann equations,

So for f(x+iy)=(x^2+y)+i(2xy-x)

I have my CR equations as:

du/dx=2x , dv/dx=2y-1

du/dy=1 , dv/dy=2x

=> 2x=2x and 2y-1= -1 , when y=0

As my first partials are continuous and exist, they satisfy the CR equations when y=0, does that mean the function is differentiable for z= x+i0? implying all real numbers?

Then does the derivative become

f'(z)= 2x -1i ?

There is no answer in the book for this, i just want to make sure i am doing it right

thanks for your help!!!