# Derivative of a Log function: Y=ln( )

1. Jul 30, 2008

### xxclaymanxx

1. Given Y = ln [ (x+1)^3/((x^2)-1)^(1/2), find y'

2. I came out with the following answer to this question:

(3x-4)/((x^2)-1)

How ever, I typed the question into an online derivative calculator (to hopefully check my asnwer as I have no answer key, and want to make sure I'm on the right path), but it came up with a completely different answer:

(2x-3)/((x^2)-1)

Could anyone point me in the right direction...my answer worked out nicely: factored, cancelled etc. but I'm worried its not correct.

Thanks for the check!

2. Jul 30, 2008

### theneedtoknow

I'm not sure how you solved the question initially, but the best way to approach such a question is to use the properties of ln.... in particular, remember that ln(a^n/b^k) = ln (a^n) - ln (b^k) and furthermore this is equal to n ln(a) - k ln(b)... Apply these same rules to the original equation and you will get a form that is extremely simple to take the derivative of, and the answer that the online derivative calculator gave you will become apparent :)