设x=1+t^2、y=cost 求 dy/dx 和d^2y/dx^2 sint-tcost/4t^3 和 sint-tcost/4t^2 哪个对?
问题描述：
设x=1+t^2、y=cost 求 dy/dx 和d^2y/dx^2 sint-tcost/4t^3 和 sint-tcost/4t^2 哪个对?
设x=1+t^2、y=cost 求 dy/dx 和d^2y/dx^2
sint-tcost/4t^3 和 sint-tcost/4t^2 哪个对?
答
∵x=1+t²,y=cost
==>dx/dt=2t,dy/dt=-sint
∴d²y/dx²=d(dy/dx)/dx
=(d((dy/dt)/(dx/dt))/dt)/(dx/dt)
=(d((-sint)/(2t))/dt)/(2t)
=((sint-tcost)/(2t²))/(2t)
=(sint-tcost)/(4t³)
故(sint-tcost)/(4t³)才是对的.