Question Detail
Question
Obtain d/dx {ln (x2 / (x2+1))}
Correct Answer
Option A is the correct answer.
Detailed Explanation
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)] = d/dx(2ln(x)) - d/dx(ln(x2+1))= 2(1/x) - (1/(x2+1)) * d/dx(x2+1)= 2/x - (1/(x2+1)) * (2x)= 2/x - 2x/(x2+1)Combine the terms by finding a common denominator:= (2(x2+1) - 2x(x)) / (x(x2+1))= (2x2 + 2 - 2x2) / (x(x2+1))= 2 / (x(x2+1)).
Hint
Simplify the logarithmic expression using log properties before differentiating.