Question Detail

First, simplify the expression using logarithm properties: ln(A/B) = ln A - ln B.ln(x2 / (x2+1)) = ln(x2) - ln(x2+1) = 2ln x - ln(x2+1).Now, differentiate with respect to x:d/dx [2ln x - ln(x2+1)] = d/dx(2ln x) - d/dx(ln(x2+1))= 2(1/x) - (1/(x2+1)) · (2x) (using the chain rule for the second term)= 2/x - 2x/(x2+1)To combine these fractions, find a common denominator:= (2(x2+1) - 2x2) / (x(x2+1))= (2x2 + 2 - 2x2) / (x(x2+1))= 2 / (x(x2+1)).