Question

x=(e^t)sint y=(e^t)cost 求d^2y/dx^2

Answer 1

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

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

dy/dx=(dy/dt)/(dx/dt)=(cost-sint)/(sint+cost)

d^2y/dx^2

=d(dy/dx)/dx

=[d(dy/dx)/dt]/[dx/dt]

={[-(sint+cost)^2-(cost-sint)^2]/(sint+cost)^2}/[(e^t)(sint+cost)]

=-2[e^(-t)]/(sint+cost)^3