求函数的二阶导数d平方y/dx平方.(1)x=1-（t平方）,y=t-（t三次方）； (2)x=ln(1+t平方),y=t-arctant

1) x=1-t^2, y=t-t^3,
=> dy/dx=(dy/dt)/(dx/dt)=(1-3t^2)/(-2t),
=> y''=d(dy/dx)/dx=d(dy/dx)/dt ÷ (dx/dt)
=[(-6t)×(-2t)-(-2)×(1-3t^2)/(-2t)^2] ÷ (-2t)
=(6t^2+2)/(-8t^3).
2) x=ln(1+t^2),y=t-arctant,
=>dy/dx=(dy/dt)/(dx/dt)=[1-1/(1+t^2)]/[2t/(1+t^2)]=t/2,
=> y''=d(dy/dx)/dx=d(dy/dx)/dt ÷ (dx/dt)
=1/2 ÷ [2t/(1+t^2)]=(1+t^2)/(4t)

求函数的二阶导数d²y/dx². (1)x=1-t²,y=t-t³； (2)x=ln(1+t²),y=t-arctant.
(1).dy/dx=(dy/dt)/(dx/dt)=(1-3t²)/(-2t)=(3t²-1)/2t
d²y/dx²=(dy′/dt)/(dx/dt)={[(12t²-2(3t²-1)]/4t²}/(-2t)=[(6t²+2)/4t²]/(-2t)=-(3t²+1)/4t³
(2). dy/dx=(dy/dt)/(dx/dt)=[1-1/(1+t²)]/[2t/(1+t²)]=t²/2t=t/2.
d²y/dx²=(dy′/dt)/(dx/dt)=(1/2)/[2t/(1+t²)]=(1+t²)/4t.