calcule a derivada?

sergio-f

a) y= x/x^2+1

b) y=(2x^3-3)^2, no ponto x= -1

eduardo-sera

y= x/x^2+1

y= x/(x²+1)

y = x . (x²+1)^(-1)

y' = (x²+1)^(-1) + x . (-1) .(x²+1)^(-2) . 2x

y' = (x²+1)^(-1) - 2x² . (x²+1)^(-2)

b) y=(2x^3-3)^2

y = (2x³ - 3)²

y' = 2.(2x³ - 3) . 3.2x²

y' = 12x²(2x³ - 3)

f ' (1) = 12.1².(2.1³ - 3)

f ' (1) = 12 . (2 - 3)

f ' (1) = -12