设 {x=2t^3+2 y=e^2t-1 ,求dy/dx,d^2y/dx^2
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利用复合函数求导法.
dy/dx=(dy/dt)/(dx/dt)=2e^(2t)/(6t^2)=e^(2t)/(3t^2)
故d^2y/dx^2=d(dy/dx)/dx=[d(dy/dx)/dt]/(dx/dt)=d[e^(2t)/(3t^2)]/dt*1/(6t^2)
=[2e^(2t)*3t^2-e^(2t)*6t]/(6t^2)
=e^(2t)*(t-1)/t
dy/dx=(dy/dt)/(dx/dt)=2e^(2t)/(6t^2)=e^(2t)/(3t^2)
故d^2y/dx^2=d(dy/dx)/dx=[d(dy/dx)/dt]/(dx/dt)=d[e^(2t)/(3t^2)]/dt*1/(6t^2)
=[2e^(2t)*3t^2-e^(2t)*6t]/(6t^2)
=e^(2t)*(t-1)/t
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