Question Detail

First, simplify the logarithm using log properties: ln(a/b) = ln(a) - ln(b) and ln(an) = n ln(a).y = ln(x2/(x+1)) = ln(x2) - ln(x+1) = 2ln(x) - ln(x+1)Now, differentiate with respect to x:dy/dx = d/dx (2ln(x)) - d/dx (ln(x+1))dy/dx = 2/x - 1/(x+1)To combine these terms, find a common denominator:dy/dx = (2(x+1) - 1*x) / (x(x+1))dy/dx = (2x + 2 - x) / (x(x+1))dy/dx = (x + 2) / (x(x+1))