`y = ln(x sqrt(x^2 - 1))` Find the derivative of the function.

`y=lnxsqrt(x^2-1)`

`y=lnx+lnsqrt[(x+1)(x-1)]`

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

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

`y'=1/x+1/[2(x+1)]+1/[2(x-1)]`

The derivative of function y is 

`y'=1/x+1/[2(x+1)]+1/[2(x-1)]`

`y=lnxsqrt(x^2-1)`

`y=lnx+lnsqrt[(x+1)(x-1)]`

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

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

`y'=1/x+1/[2(x+1)]+1/[2(x-1)]`

The derivative of function y is 

`y'=1/x+1/[2(x+1)]+1/[2(x-1)]`