求dy比dx和dy的平方比dx的平方 190
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y + e^(x+y) - 2x = 0, 两边对 x 求导， 注意 y = y(x),
dy/dx + e^(x+y)(1+dy/dx) - 2 = 0 (1),
解得 dy/dx = [2-e^(x+y)]/[1+e^(x+y)] （2) ;
式隐洞哪 (1) 两边再对颤袭 x 求导， 得
d^2y/dx^2 + e^(x+y)(1+dy/dx)^2 + e^(x+y)(d^2y/dx^2) = 0
解得 d^2y/dx^2 = [-e^(x+y)(1+dy/dx)^2]/[1+e^(x+y)]， 式(2)代入， 得
d^2y/dx^2 = [-e^(x+y)[1+e^(x+y)+2-e^(x+y)]^2/[1+e^(x+y)]^3}
= -9e^(x+y)/灶码[1+e^(x+y)]^3
dy/dx + e^(x+y)(1+dy/dx) - 2 = 0 (1),
解得 dy/dx = [2-e^(x+y)]/[1+e^(x+y)] （2) ;
式隐洞哪 (1) 两边再对颤袭 x 求导， 得
d^2y/dx^2 + e^(x+y)(1+dy/dx)^2 + e^(x+y)(d^2y/dx^2) = 0
解得 d^2y/dx^2 = [-e^(x+y)(1+dy/dx)^2]/[1+e^(x+y)]， 式(2)代入， 得
d^2y/dx^2 = [-e^(x+y)[1+e^(x+y)+2-e^(x+y)]^2/[1+e^(x+y)]^3}
= -9e^(x+y)/灶码[1+e^(x+y)]^3
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