求函数z=x+y分之xy的全微分 z = xy/(x+y)dz =[(x+y)d(xy) - xyd(x+y) ]/(x+y)^2 =[(x+y)(xdy+ydx) - xy(dx+dy) ]/(x+y)^2 ={ [ (x+y)y - xy] dx + [(x+y)x- xy ] dy }/(x+y)^2 =(y^2.dx + x^2.dy)/(x+y)^2
dz=d(x+y+xy)=dx+dy+d(xy)
=dx+dy+ydx+xdy
=(1+y)dx+(1+x)dy
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