{x=e右上角tcost, 则 dy⼀dx = {y=e右上角tsint,

2025-05-20 09:59:10
推荐回答(2个)
回答1:

这是参数方程求导
x=e^(t cost)
y=e^(t sint)
x'(t)=e^(t cost)*(cost-tsint)
y'(t)=e^(t sint)*(sint+tcost)
dy/dx =y'(t)/x'(t)=[e^(t sint)*(sint+tcost)]/[e^(t cost)*(cost-tsint)]

回答2:

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