I need to simplify it further, but before I do I checked it into Mathematica and it says the derivative is incorrect. What did I do wrong?
I find it to be a bit easier, though there is more factoring involved, if you divide by x first:
Now for the derivative:
I find this result to be reasonably adequate, but your text decided differently and cleared the fraction in the denominator. So, using a little trick:
-Dan