Question

求由参数方程x=acost;y=bsint所确定的函数的二阶导数d^2y/dx^2,急需要详细步骤，谢谢！！

Answer 1

φ(t)=acost,ψ(t)=bsint,φ'(t)=-asint,ψ'(t)=bcost,φ"(t)=-acost,ψ"(t)=-bsint,φ'3(t)=asint

故d^2y/dx^2=（-abcost*cost-absint*sint)/asint=-b/sint

Answer 2

先求一阶：dy/dx=dy/dt除以dx/dt=bcost/-asint=-bcott/a 再求二阶=d(dy/dx)/dx=d(-bcott/a)/dx=d(-bcott/a)/dt除以dx/dt=bcsc^2t/-asint=结果，楼主自己化简吧，用手机打得太费劲了。

Answer 3

dy/dx=(dy/dt)/(dx/dt)=bcost/(-asint)=-bcott/a
d²y/dx²=d(dy/dx)/dx=[d(dy/dx)/dt]/(dx/dt)=（b/asin²t)/(-asint)
=-b/a²sin³t