Question Detail

Let y = ln(x2 / (x2 + 1)).First, simplify using logarithm properties: ln(a/b) = ln(a) - ln(b).y = ln(x2) - ln(x2 + 1)y = 2ln(x) - ln(x2 + 1)Now, differentiate with respect to x:dy/dx = d/dx [2ln(x)] - d/dx [ln(x2 + 1)]dy/dx = 2 * (1/x) - (1/(x2 + 1)) * (2x) (using chain rule for ln(u) derivative)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))Therefore, the correct option is A.