参数方程x=2t-1,te^y+y+1=0,求d^2y/dx^2 (x=0)

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参数方程x=2t-1,te^y+y+1=0,求d^2y/dx^2 (x=0)
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参数方程x=2t-1,te^y+y+1=0,求d^2y/dx^2 (x=0)
参数方程x=2t-1,te^y+y+1=0,求d^2y/dx^2 (x=0)

参数方程x=2t-1,te^y+y+1=0,求d^2y/dx^2 (x=0)
dx/dt=2;
te^y+y+1=0,关于t求导,得e^y+te^y*(dy/dt)=0,得dy/dt=-1/t;
所以dy/dx=(dy/dt)/(dx/dt)=-1/(2t).
所以d^2y/dx^2=[d(dy/dx)]/dx={[d(dy/dx)]/dt}/(dx/dt)=[1/(2t^2)]/2=1/(4t^2).
当x=0时,t=1/2,那么d^2y/dx^2(x=0)=1.