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First, use logarithm properties to simplify the expression before differentiating:ln(x2 / (x2 + 1)) = ln(x2) - ln(x2 + 1)Further simplify ln(x2) = 2ln(x).So the expression becomes: 2ln(x) - ln(x2 + 1).Now differentiate term by term:d/dx(2ln(x)) = 2 * (1/x) = 2/xd/dx(ln(x2 + 1)) requires the chain rule: d/dx(ln(u)) = u'/u. Here u = x2 + 1, so u' = 2x.d/dx(ln(x2 + 1)) = 2x / (x2 + 1)Combine the derivatives:d/dx ln(x2 / (x2 + 1)) = 2/x - 2x / (x2 + 1)Find a common denominator to combine the fractions:= (2(x2 + 1) - 2x * x) / (x(x2 + 1))= (2x2 + 2 - 2x2) / (x(x2 + 1))= 2 / (x(x2 + 1))This matches option A.