按求导法则按部就班地求就是：y'=[x'(1+x²)-x*(1+x²)']/(1+x²)²=(1-x²)/(1+x²)²；y"=[(1-x²)'(1+x²)²-(1-x²)((1+x²)²)']/[(1+x²)²]²=[-2x(1+x²)-(1-x²)*2*2x]/(1+x²)³=2x(x²-3)/(1+x²)³；
