Question Detail

First, simplify the logarithmic expression using the property ln(a⁄b) = ln a - ln b, which gives ln(x2) - ln(x2+1). This can be further written as 2ln|x| - ln(x2+1). Now, differentiate each term. The derivative of 2ln|x| is 2/x. The derivative of ln(x2+1) using the chain rule is (1⁄(x2+1)) * (2x) = 2x⁄(x2+1). Subtracting these gives 2/x - 2x⁄(x2+1). Combining them with a common denominator, x(x2+1), results in (2(x2+1) - 2x2) ⁄ (x(x2+1)) = (2x2 + 2 - 2x2) ⁄ (x(x2+1)) = 2 ⁄ (x(x2+1)).