Question Detail

First, simplify the logarithmic function using log properties: y = ln(x² / (x+1)) = ln(x²) - ln(x+1) = 2 ln x - ln(x+1).Now differentiate with respect to x: dy/dx = d/dx(2 ln 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 into a single fraction: dy/dx = (2(x+1) - x) / (x(x+1)) = (2x + 2 - x) / (x(x+1)) = (x+2) / (x(x+1)).