x^2y+y^2x＝1的微分怎么求
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x^(2y) + y^(2x) = 1
e^(2ylnx) + e^(2xlny) = 1
2(y'lnx+y/x)e^(2ylnx) + 2(lny + xy'/y)e^(2xlny) = 0
(y'xlnx+y)x^(2y) + (ylny + xy')y^(2x) = 0
y' = -[yx^(2y)+ylny y^(2x)]/[xlnx x^(2y)+xy^(2x)]
dy = {-[yx^(2y)+ylny y^(2x)]/[xlnx x^(2y)+xy^(2x)]}dx
e^(2ylnx) + e^(2xlny) = 1
2(y'lnx+y/x)e^(2ylnx) + 2(lny + xy'/y)e^(2xlny) = 0
(y'xlnx+y)x^(2y) + (ylny + xy')y^(2x) = 0
y' = -[yx^(2y)+ylny y^(2x)]/[xlnx x^(2y)+xy^(2x)]
dy = {-[yx^(2y)+ylny y^(2x)]/[xlnx x^(2y)+xy^(2x)]}dx
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