设函数y=f(x)由方程e2x+y一 cos(xy)=e一1所确定,则曲线y=f(x)在点(0,1)处的法线方程为________.

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问题 设函数y=f(x)由方程e2x+y一 cos(xy)=e一1所确定,则曲线y=f(x)在点(0,1)处的法线方程为________.

选项

答案x一2y+2=0.

解析 方程e2x+y—cos(xy)=e一1两边对x求导得
(2+y’)e2x+y+sin(xy)(y+xy’)=0
将x=0,y=1代入上式得y’=一2.
则y=f(x)在(0,1)处的法线方程为y一1=
即  x一2y+2=0.
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