Simplifying the derivative of f(x)=2√(x²+1)/(x-1)

[Emethyst]

Homework Statement

Sketch the graph of the function f(x)=(2(x^2+1)^1/2)/(x-1)

Homework Equations

All the derivative simplification rules

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 similar question like this in my homework questions. Thanks in advance.

 

[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.