参数方程x=e的t次方*cost.y=e的t次方*sint求其导数及二阶导数

导数：
dy/dx=[e^(t·sint)]'/[e^(t·cost)]'=[sint·tcost·e^(t·sint)]/[-cost·tsint·e^(t·cost)]
二阶导数：
y"
={[sint·tcost·e^(t·sint)]'·[-cost·tsint·e^(t·cost)]-[-cost·tsint·e^(t·cost)]‘·[sint·tcost·e^(t·sint)]}
/[-cost·tsint·e^(t·cost)]³
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我已经晕了，剩下的楼主自己化简吧

因为
dx/dt=e^t * (cost - sint)
dy/dt=e^t * (sint + cost)
所以根据公式
dy/dx=(dy/dt)/(dx/dt)
=(sint + cost)/(cost - sint)
=(tant+1)/(1-tant)
=tan(t+π/4)
另外有
d(dy/dx)/dt=(sec(t + π/4))^2
所以d2y/dx2=(d(dy/dx)/dt) / (dx/dt)
=(sec(t + π/4))^2 / [e^t * (cost - sint)]
=(1/2) * (√2 ) * e^(-t) * (sec(t + π/4))^3