Thread: Is there a trick for higher derivatives?

Wow. I clicked quote instead of edit. My bad.

$\displaystyle f(x) = \frac{x^2-2x+4}{x-2}$

$\displaystyle f'(x)= \frac{x(x-4)}{(x-2)^2}$

After I take the first derivative and I need the second, I can get a second derivative but it takes freakin' forever and my test only lasts for about an hour. I was wondering if anyone knew of a fast trick or some creative ways to deal with this problem and minimize time computing it? 'Cause I swear, I don't want to waste forever just getting this when I have to sketch 10 other functions on my examination.

$\displaystyle \frac{x^2-2x+4}{x-2} = \frac{x(x-2)+4}{x-2} = x + \frac{4}{x-2}$, if that helps.