求下列参数方程所表示的函数y-y(x)的导数dy/dx:
(1)
{x=t2+1,
{y=t3+t;
(2)
{x=cosθ,
{y=2sinθ;
(3)
{x=t/(1+t2),
{y=t2/(1+t2);
(4)
{x=t-ln(1+t),
{y=t3+t2.
(1)dy/dx=(dy/dt)/(dx/dt)=(3t2+1)/2t (2)dy/dx=(dy/dθ)/(dx/dθ)=2cosθ/-sinθ=2cotθ, (3)dy/dx=(dy/dt)/(dx/dt)={[2t(1+t2-t22t)]/(1+t2)2}/[(1+t2-t•2t]/(1+t2)2]=2t/(1-t2) (4)dy/dx=(dy/dt)/(dx/dt)=(3t2+2t)/[1-1/(1+t)]=(3t+2)(1+t)