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.

You're doin it wrong.

f'(x) = lim[{(2z^2-1) - (2x^2-1)}/(z-x),{z->x}]
      = lim[2(z^2 - x^2)/(z-x),{z->x}]
      = 2 lim[z+x,{z->x}]
      = 2 (2x)
      = 4x