Derivatives of complex functions

Okay,

I am doing kind of an advanced study thing in one of my calculus courses and I've done pretty well on all the objectives up until this one. I am completely lost when it comes to this.

My objective is to show that for the complex function $\displaystyle f(z)=\overline{z}$, $\displaystyle f'(z)$ does not exist at any point.

So from my brief reading in Schaum's Outline on Advanced Calculus (the only book in the whole library about advanced calc), I know that complex functions can be written as functions of x and y. So, $\displaystyle f(z)=u(x,y)+iv(x,y)$. I know that $\displaystyle f(z)=\overline{z}$ is the conjugate...and that's where I get stuck. I've read about the Cauchy-Riemann equations and how to determine if a function is analytic, and I know that in the complex plane we can approach a particular point from any direction, like in multivariable calc.

So basically, I'm just lost...can anyone try to break this down for me? I'm just not understanding how to work with these complex functions.

Any help is GREATLY appreciated!