# Homework Help: Finding the derivative

1. Apr 3, 2009

### Emethyst

1. The problem statement, all variables and given/known data
Sketch the graph of the function f(x)=(2(x^2+1)^1/2)/(x-1)

2. Relevant equations
All the derivative simplification rules

3. The attempt at a solution
The only part of the question I need help with here is finding the derivative of this function. In my book it says the derivative is f'(x)=(-3(x+1))/((x-1)^2(x^2+1)^1/2), but all I can get is f'(x)=(2x(x-1)-2(x^2+1)^1/2)/((x-1)^2(x^2+1)^1/2). I don't know how to go about simplifying this any further. Any help on this would be greatly appreicated, as I have a similiar question like this in my homework questions. Thanks in advance.

2. Apr 3, 2009

### n!kofeyn

Either the book is wrong or you have a typo, as the 3 should be a 2. The derivative is
$$f'(x) = \frac{-2(x+1)}{(x-1)^2 \sqrt{x^2+1}}$$

It looks like you did the derivative correctly, except that the first 1/2 you encounter when reading your solution should be a 1. This comes from when you found the common denominator, and you will be able to further simplify the derivative after this change.