设x=u.e^u,u^2+v^2=1,求dv/dx;求详解

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设x=u.e^u,u^2+v^2=1,求dv/dx;求详解

设x=u.e^u,u^2+v^2=1,求dv/dx;求详解
设x=u.e^u,u^2+v^2=1,求dv/dx;求详解

设x=u.e^u,u^2+v^2=1,求dv/dx;求详解
x = ue^u
两边微分:
dx = e^udu + ue^udu = [(1+u)e^u]du
du/dx = 1/[(1+u)e^u]
u^2+v^2=1
两边微分:
2udu + 2vdv = 0
dv/du = -u/v
dv/dx = (dv/du)(du/dx)
=(-u/v){1/[(1+u)e^u]}
=-u/[v(1+u)e^u]