Trouble with derivatives

f(x)=2x^2 - 1
I got to:
f'(x)=lim z->x (2z^2 - 2x^2 - 2)/(z-x)
Problem is, I can't seem to factor (z-x) out of the numerator. I was just wondering if I had missed something or done my derivative wrong. Any help would be much appreciated.

f(x)=2*x^2 - 1

When your variable is raised to a power of n, the derivative is pretty simple. a is constant.

d_a*x^n = a*n*x^(n-1) dx

fuck all of that other stuff.  learn your derivative rules.