Ableiten mit Quotientenregel:
y'' = (4x^3 - 12x) / (x^2 + 1)^3
u = 4x^3 - 12x
u' = 12x^2 - 12
v = (x^2 + 1)^3
v' = 3(1 + x^2)^2·2x = 6x·(x^2 + 1)^2
y''' = ((12x^2 - 12)·(1 + x^2)^3 - (4x^3 - 12x)·6x·(x^2 + 1)^2) / (1+x^2)^6
y''' = ((12x^2 - 12)·(1 + x^2) - (4x^3 - 12x)·6x) / (1+x^2)^4
y''' = ((12x^4 - 12) - (24x^4 - 72x^2)) / (1+x^2)^4
y''' = (- 12x^4 + 72x^2 - 12) / (1+x^2)^4