Given: `g(x)=ln(xsqrt(x^2-1))`

Rewrite the equation using the Law of exponents. Then find the derivative.

`g(x)=lnx+(1)/(2)ln(x^2-1)`

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

The derivative is:

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

Given: `g(x)=ln(xsqrt(x^2-1))`

Rewrite the equation using the Law of exponents. Then find the derivative.

`g(x)=lnx+(1)/(2)ln(x^2-1)`

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

The derivative is:

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