Question Detail

First, use logarithm properties to simplify the expression: ln(a/b) = ln(a) - ln(b) and ln(xn) = n ln(x).So, 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)] = 2 * (1/x) - (1/(x2+1)) * d/dx(x2+1)= 2/x - (1/(x2+1)) * (2x)= 2/x - 2x/(x2+1)To combine these terms, find a common denominator:= (2(x2+1) - 2x * x) / (x(x2+1))= (2x2 + 2 - 2x2) / (x(x2+1))= 2 / (x(x2+1)).