Assume log≡ln.
y=ln{(√(x+1)+√(x-1))/(√(x+1)-√(x-1))}
First rationalise the argument by multiplying top and bottom by √(x+1)+√(x-1)
(√(x+1)+√(x-1))2/((x+1)-(x-1))=(x+1+2√(x2-1)+x-1)/2=x+√(x2-1).
y=ln(x+√(x2-1)),
dy/dx=(1/(x+√(x2-1))(1+x/√(x2-1))=
(1/(x+√(x2-1))(x+√(x2-1))/√(x2-1))=1/√(x2-1)).