设xy+lny+lnx=1,求dy/dx│x=1x=1则y+lny+0=1y+lny=1所以y=1dxy+dlny+dlnx=0xdy+ydx+(1/y)dy+(1/x)dx=0(x+1/y)dy=-(y+1/x)dxx=y=1所以2dy=2dx所以原式=1xdy+ydx+(1/y)dy+(1/x)dx=0这一步不会!怎么来的?

Question

设xy+lny+lnx=1,求dy/dx│x=1 x=1则y+lny+0=1y+lny=1所以y=
1dxy+dlny+dlnx=0xdy+ydx+(1/y)dy+(1/x)dx=0(x+1/y)dy=-(y+1/x)dxx=y=1所以2dy=2dx所以原式=1
【xdy+ydx+(1/y)dy+(1/x)dx=0】这一步不会!怎么来的?

Answer 1

凑微分的过程!