求导数,,详解,第三小问
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x=ln(1+t^2)
dx/dt = 2t/(1+t^2)
y=t-arctant
dy/dt =1 - 1/(1+t^2) = t^2/(1+t^2)
dy/dx
= (dy/dt)/(dx/dt)
= t/2
d/dt (dy/dx ) = 1/2
d^2y/dx^2
=[d/dt (dy/dx ) ]/ ( dx/dt)
=(1/2)/[2t/(1+t^2)]
=(1+t^2)/(4t)
dx/dt = 2t/(1+t^2)
y=t-arctant
dy/dt =1 - 1/(1+t^2) = t^2/(1+t^2)
dy/dx
= (dy/dt)/(dx/dt)
= t/2
d/dt (dy/dx ) = 1/2
d^2y/dx^2
=[d/dt (dy/dx ) ]/ ( dx/dt)
=(1/2)/[2t/(1+t^2)]
=(1+t^2)/(4t)
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