Question

求微分的题目一道,x=e^(-t)sint,y=e^tcost,求 d^2y/dx^2

Answer 1

dx/dt=-e^(-t)sint+e^(-t)cost=e^(-t)(cost-sint)

dy/dt=e^tcost+e^t(-sint)=e^t(cost-sint)

dy/dx=(dy/dt)/(dx/dt)=e^(2t)

d(dy/dx)/dt=2e^(2t)

d^2y/dx^2=d(dy/dx)/dx=[d(dy/dx)/dt]/(dx/dt)=2e^(3t)/(cost-sint)