Question Detail

First, use logarithm properties to simplify the expression:ln(x2 / (x2+1)) = ln(x2) - ln(x2+1) = 2ln|x| - ln(x2+1).Now, differentiate with respect to x:d/dx (2ln|x| - ln(x2+1)) = 2 * (1/x) - (1/(x2+1)) * (2x)= 2/x - 2x/(x2+1).To combine these terms, find a common denominator:= (2(x2+1) - 2x*x) / (x(x2+1))= (2x2 + 2 - 2x2) / (x(x2+1))= 2 / (x(x2+1)).This matches option A. (Option B is identical to A, so both A and B are technically correct based on the options provided in the image).