求解:设方程xy+e的x次方lny=1确定了函数y(x),则y'(0)=? A.-e(1+e) B.-1 C.e(1+e) D.1

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求解:设方程xy+e的x次方lny=1确定了函数y(x),则y'(0)=? A.-e(1+e) B.-1 C.e(1+e) D.1
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求解:设方程xy+e的x次方lny=1确定了函数y(x),则y'(0)=? A.-e(1+e) B.-1 C.e(1+e) D.1
求解:设方程xy+e的x次方lny=1确定了函数y(x),则y'(0)=? A.-e(1+e) B.-1 C.e(1+e) D.1

求解:设方程xy+e的x次方lny=1确定了函数y(x),则y'(0)=? A.-e(1+e) B.-1 C.e(1+e) D.1
方程两边对y求导
(xy')+(e^xlny)'=0
(y+y')+(e^xlny+e^x*y'/y)=0
当x=0时 y=1
将x=0,y=1代入得到(1+y')+(1+y')=0
y'(0)=-1