高数隐函数二阶求导
最新回答
敷衍丶换来无言的结局ゝ
2023-05-26 21:54:58
y'= e^y + (xe^y)y'
(1-xe^y)y' = e^y
y' =e^y/(1-xe^y)
y''
=[e^y/(1-xe^y)]y' - [ e^y/(1-xe^y)^2] .[ -e^y - xe^y.y']
=[e^y/(1-xe^y)].[e^y/(1-xe^y)] - [ e^y/(1-xe^y)^2] .{ -e^y - xe^y.[e^y/(1-xe^y)] }
=e^(2y)/(1-xe^y)^2 - [ e^y/(1-xe^y)^2] .[ -e^y /(1-xe^y)]
=e^(2y)/(1-xe^y)^2 + e^(2y)/(1-xe^y)^3
若樱落如烟
2023-06-15 20:53:18
y'=e^y+y'xe^y
y'(1-xe^y)=e^y
y''(1-xe^y)-y'(e^y+y'xe^y)=y'e^y
y''(1-xe^y)-y'y'=y'e^y
y''(1-xe^y)-[e^y/(1-xe^y)]^2=e^2y/(1-xe^y)
y''=e^2y/(1-xe^y)^3+e^2y/(1-xe^y)^2
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