Question

differentiate the function ln(x(sqr root x^2-1))

Answer 1

\[
\ln(x\sqrt{x^2-1}) = \ln(x) + \ln(\sqrt{x^2-1})=\ln(x) + \frac{1}{2}\ln(x^2-1)
\]

Answer 2

Then use chain rule.

Answer 3

Or without chain rule: \[
\ln(x) + \frac{1}{2}\ln(x^2-1) = \ln(x)+\frac{1}{2}\ln[(x-1)(x+1)] = \ln(x)+\frac{1}{2}\ln(x-1)+\frac{1}{2}\ln(x+1)
\]

Answer 4

\[
\ln(x)+\frac{1}{2}\ln(x-1)+\frac{1}{2}\ln(x+1)
\]

Answer 5

thanx

Answer 6

just a note, differentiating ln (x-1) is still a chain rule.

Answer 7

thanx