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)]