求y=sin2x/(1+cosx)的导数或微分
问题描述：
求y=sin2x/(1+cosx)的导数或微分
答
y=sin2x/(1+cosx)
=2cosx*sinx/(1+cosx)
=2cosxtan(x/2)
y'=2tan(x/2)*(-sinx)+2cosx*sec²(x/2)*1/2
=cosxsec²(x/2)-2sinxtan(x/2)
=2cosx-2/(1+cosx)
微分：dy=[2cosx-2/(1+cosx)]dx
x=tcost,y=tsint
dx/dt=cost+t(-sint)=cost-tsint
dy/dt=sint+tcost=sint+tcost
dy/dx=(dy/dt)/(dx/dt)
=(sint+tcost)/(cost-tsint)