高数一道求导的题目，有图求大神解答
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x=te^(-t)
dx/dt =(1-t).e^(-t)
y=e^t
dy/dt =e^t
dy/dx =(dy/dt)/(dx/dt) =e^t/[(1-t).e^(-t)] = e^(2t)/(1-t)
d/dt (dy/dx)
=d/dt [e^(2t)/(1-t) ]
=[ 1/(1-t)^2 + 2/(1-t) ] e^(2t)
=[(3-2t)/(1-t)^2 ].e^(2t)
d^2y/dx^2
=d/dt [e^(2t)/(1-t) ] /(dx/dt)
=[(3-2t)/(1-t)^2 ].e^(2t) /[(1-t).e^(-t)]
=[(3-2t)/(1-t)^3 ].e^(3t)
dx/dt =(1-t).e^(-t)
y=e^t
dy/dt =e^t
dy/dx =(dy/dt)/(dx/dt) =e^t/[(1-t).e^(-t)] = e^(2t)/(1-t)
d/dt (dy/dx)
=d/dt [e^(2t)/(1-t) ]
=[ 1/(1-t)^2 + 2/(1-t) ] e^(2t)
=[(3-2t)/(1-t)^2 ].e^(2t)
d^2y/dx^2
=d/dt [e^(2t)/(1-t) ] /(dx/dt)
=[(3-2t)/(1-t)^2 ].e^(2t) /[(1-t).e^(-t)]
=[(3-2t)/(1-t)^3 ].e^(3t)
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