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To differentiate ln(x2 / (x2 + 1)), first use logarithm properties to simplify the expression:ln(x2 / (x2 + 1)) = ln(x2) - ln(x2 + 1) = 2 ln x - ln(x2 + 1).Now differentiate with respect to x:d/dx [2 ln x - ln(x2 + 1)] = d/dx(2 ln x) - d/dx(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) - 2x2] / [x(x2 + 1)]= [2x2 + 2 - 2x2] / [x(x2 + 1)]= 2 / (x(x2 + 1)).