## anonymous 4 years ago Differentiate the function g(x) = ln [x*sqrt(x^2 - 1)]

1. anonymous

$g(x) = \ln (x \sqrt(x^2 - 1))$ this one?

2. anonymous

use chain rule

3. anonymous

start with $\ln(x)+\frac{1}{2}\ln(x+1)+\frac{1}{2}\ln(x-1)$ and it will be easier

4. anonymous

sooo g'(x) = 1/x + 1/x(x+1) + 1/x(x-1) ?

5. anonymous

stupid i know but i'm having trouble simplifying that what do i do

6. anonymous

g'(x) = 1/x + 1/2(1/(x+1)) + 1/2(1/(x-1)) = 1/x + 1/2(x+1) + 1/2(x-1)

7. anonymous

well yeah i got that sorry i typed it wrong but i need to simplify that