Exercícios 8.2 Determine a derivada. y = x arc tg x f (x) = arc sen 3x g (x) = arc sen x3 y = arc tg x2 y = 3 arc tg (2x + 3) y = arc sen ex y = e3...

Vamos determinar as derivadas das funções dadas: 1. y = x arctg x y' = arctg x + x * 1/(1+x²) 2. f(x) = arcsen(3x) f'(x) = 3 / sqrt(1 - (3x)²) 3. g(x) = arcsen(x³) g'(x) = 3x² / sqrt(1 - x⁶) 4. y = arctg(x²) y' = 2x / (1 + x⁴) 5. y = 3arctg(2x + 3) y' = 6 / (4x² + 12x + 9) 6. y = arcsen(e^x) y' = e^x / sqrt(1 - e^(2x)) 7. y = e^(3x) arcsen(2x) y' = 6xe^(3x) / sqrt(1 - 4x²) + 2e^(3x)arcsen(2x) 8. y = x²earctg(2x) y' = 2xarctg(2x) + x² * 2/(1 + 4x²) 9. y = e^(-3x) + ln(arctg(x)) y' = -3e^(-3x) + 1/(xln(10) * (1 + x²))