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Let y = ln(x2 / (x2 + 1)).First, use the logarithm property ln(a/b) = ln(a) - ln(b):y = ln(x2) - ln(x2 + 1)Further simplify using ln(ap) = p ln(a):y = 2 ln(x) - ln(x2 + 1)Now, differentiate with respect to x:dy/dx = d/dx(2 ln(x)) - d/dx(ln(x2 + 1))Using the chain rule, d/dx(ln(u)) = (1/u) du/dx:dy/dx = 2 * (1/x) - (1 / (x2 + 1)) * d/dx(x2 + 1)dy/dx = 2/x - (1 / (x2 + 1)) * (2x)dy/dx = 2/x - (2x / (x2 + 1))To combine these terms, find a common denominator:dy/dx = (2(x2 + 1) - 2x * x) / (x(x2 + 1))dy/dx = (2x2 + 2 - 2x2) / (x(x2 + 1))dy/dx = 2 / (x(x2 + 1))