x=2(t-sint) y=3(1-cost)求d^2y/dx^2【如图】求解 谢谢！
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x=2(t-sint)
dx/dt =2(1-cost)
y=3(1-cost)
dy/dt =3sint
dy/dx =(dy/dt)/(dx/dt) =(3/2)[sint/(1-cost)]
d/dx(dy/dx)
=(3/2){ [(1-cost)cost - sint.(sint) ]/(1-cost)^2 }
=(3/2) [(cost -1)/(1-cost)^2 ]
=-(3/2) [1/(1-cost)]
d^2y/dx^2
=d/dx(dy/dx) /(dx/dt)
=-(3/2) [1/(1-cost)] /[2(1-cost)]
=-(3/4) [1/(1-cost)^2]
dx/dt =2(1-cost)
y=3(1-cost)
dy/dt =3sint
dy/dx =(dy/dt)/(dx/dt) =(3/2)[sint/(1-cost)]
d/dx(dy/dx)
=(3/2){ [(1-cost)cost - sint.(sint) ]/(1-cost)^2 }
=(3/2) [(cost -1)/(1-cost)^2 ]
=-(3/2) [1/(1-cost)]
d^2y/dx^2
=d/dx(dy/dx) /(dx/dt)
=-(3/2) [1/(1-cost)] /[2(1-cost)]
=-(3/4) [1/(1-cost)^2]
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