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,

题目

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,

答案

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