Question

求下列参数方程的导数？

Answer 1

(13)
x=a(cost+tsint)
dx/dt = a(-sint +sint +tcost)= atcost
y=a(sint-tcost)
dy/dt =a(cost -cost +tsint)= atsint
dy/dx =(dy/dt)/(dx/dt) = tant
(10)
x=e^(t^2)
dx/dt = 2t.e^(t^2)
y=te^t
dy/dt = (1+t)e^t
dy/dx =(dy/dt)/(dx/dt) = [(1+t)/(2t)].e^(t-t^2)
(13)
x=(a/2)( t+ 1/t)
dx/dt =(a/2)( 1- 1/t^2)
y=(b/2)(t-1/t)
dy/dt =(b/2)(1+1/t^2)
dy/dx =(dy/dt)/(dx/dt) = (b/a)[(t^2+1)/(t^2-1)]