设y=2arctan(y/x),求dy/dx,d²y/dx². 　　设F(x,y)=y-2arctan(y/x)=0,则 　　dy/dx=-(∂F/∂x)/(∂F/∂y)=-[2(y/x²)/(1+y²/x²)]/[(1-2/x)/(1+y²/x²)] 　　=-[2y/(x²+y²)]/[x(x-2)/(x²+y²)]=-2y/[x(x-2)] 　　d²y/dx²=[-2(x²-2x)(dy/dx)+2y(2x-2)]/(x²-2x)² 　　=[4y+2y(2x-2)]/(x²-2x)²=4(y+xy-y)/(x²-2x)²