y = 1/(1 + x²) y' = - (1 + x²)'/(1 + x²)² = - 2x/(1 + x²)² y'' = - 2 • [(1 + x²)² - x • 2(1 + x²) • 2x]/(1 + x²)⁴ = - 2 • [1 + x² - 4x²]/(1 + x²)³ = - 2(1 - 3x²)/(1 + x²)³ = 2(3x² - 1)/(1 + x²)³
