Question Detail
Question
Find d/dx (ln(x²/(x+1)))
Correct Answer
Option D is the correct answer.
Detailed Explanation
First, use logarithm properties to simplify the expression before differentiating:y = ln(x²/(x+1)) = ln(x²) - ln(x+1)y = 2ln(x) - ln(x+1)Now, differentiate y with respect to x:dy/dx = d/dx (2ln(x)) - d/dx (ln(x+1))dy/dx = 2 * (1/x) - 1/(x+1) * d/dx(x+1)dy/dx = 2/x - 1/(x+1)Combine the terms by finding a common denominator:dy/dx = (2(x+1) - x) / (x(x+1))dy/dx = (2x + 2 - x) / (x(x+1))dy/dx = (x + 2) / (x(x+1)).
Hint
Use logarithm properties to simplify the expression before taking the derivative: ln(a/b) = ln(a) - ln(b) and ln(a^n) = n ln(a).