dy= (y(x))'= (ln ((x+1)/(2x²-1)))'= 1/((x+1)/(2x²-1)) * ((x+1)/(2x²-1))'= (2x²-1)/(x+1) * ((x+1)'(2x²-1)-(x+1)(2x²-1)')/(2x²-1)²= (2x²-1)/(x+1) * (2x²-1-4x²-4x)/(2x²-1)²= (2x²-1)/(x+1) * (-2x²-4x-1)/(2x²-1)² = (-2x²-4x-1)/(x+1)(2x²-1)= (2x²+4x+1)/(x+1)(1-2x²)
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dy= (y(x))'= (ln ((x+1)/(2x²-1)))'= 1/((x+1)/(2x²-1)) * ((x+1)/(2x²-1))'= (2x²-1)/(x+1) * ((x+1)'(2x²-1)-(x+1)(2x²-1)')/(2x²-1)²= (2x²-1)/(x+1) * (2x²-1-4x²-4x)/(2x²-1)²= (2x²-1)/(x+1) * (-2x²-4x-1)/(2x²-1)² = (-2x²-4x-1)/(x+1)(2x²-1)= (2x²+4x+1)/(x+1)(1-2x²)