y=y(x)由参数方程x=2t/(1+t^);y=(1-t^2)/1+t^2确定,求dy/dx

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y=y(x)由参数方程x=2t/(1+t^);y=(1-t^2)/1+t^2确定,求dy/dx
y=y(x)由参数方程x=2t/(1+t^);y=(1-t^2)/1+t^2确定,求dy/dx

y=y(x)由参数方程x=2t/(1+t^);y=(1-t^2)/1+t^2确定,求dy/dx
dx/dt=2[(1+t^2-2t^2]/(t+t^2)^2=2(1-t^2)/(1+t^2)^2
dy/dt=[-2t(1+t^2)-(1-t^2)*2t]/(1+t^2)^2=-4t/(1+t^2)^2
因此dy/dx=(dy/dt)/(dx/dt)=-2t/(1-t^2)