I am going over some of my notes, and I was taking a different way to get to the definition.

Find the slopes between two points, x - h AND x + h. We want the "slope" or derivative at x, so set the limit as h approaches zero. How do I use algebra to go from this:

$\displaystyle lim_{h\rightarrow 0} \frac{f(x+h)-f(x-h)}{2h}$

To this:

$\displaystyle lim_{h\rightarrow 0} \frac{f(x+h)-f(x)}{h}$