设参数方程x=t-In(1+t^2) y=arctant 确定函数y=y(x),求d^2y/dx^2

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设参数方程x=t-In(1+t^2) y=arctant 确定函数y=y(x),求d^2y/dx^2

设参数方程x=t-In(1+t^2) y=arctant 确定函数y=y(x),求d^2y/dx^2
设参数方程x=t-In(1+t^2) y=arctant 确定函数y=y(x),求d^2y/dx^2

设参数方程x=t-In(1+t^2) y=arctant 确定函数y=y(x),求d^2y/dx^2
dx/dt=1-2t/(1+t^2)=(1+t^2-2t)/(1+t^2)=(t-1)^2/(1+t^2)
dy/dt=1/(1+t^2)
y'=1/(t-1)^2
dy'/dt=-2/(t-1)^3
y"=(dy'/dt)/(dx/dt)=-2(1+t^2)/(t-1)^5