Hey, I need help with the following problem:

Differentiate the function:

g(x)=ln(x*(x^2 - 1)^1/2)

Thanks!

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- Jan 24th 2008, 12:35 PMluckeyduckHelp with finding the derivative of a logarithmic function
Hey, I need help with the following problem:

Differentiate the function:

g(x)=ln(x*(x^2 - 1)^1/2)

Thanks! - Jan 24th 2008, 12:55 PMJhevon
now this is doable by the chain rule. but it is easier to simplify first

note that $\displaystyle \ln \left[ x (x^2 - 1)^{1/2} \right] = \ln \left[ x (x + 1)^{1/2} (x - 1)^{1/2} \right] = \ln x + \frac 12 \ln (x + 1) + \frac 12 \ln (x - 1)$

now you can differentiate each of those terms, right?