a) y= x/x^2+1
b) y=(2x^3-3)^2, no ponto x= -1
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
Comments
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