曲线ex+y-sin(xy)=e在点(0,1)处的切线为________.

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问题 曲线ex+y-sin(xy)=e在点(0,1)处的切线为________.

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答案y=(1/e-1)x+1

解析 ex+y-sin(xy)=e两边对x求导得ex+y(1+dy/dx)-cos(xy)(y+xdy/dx)=0,将x=0,y=1代入上式得dy/dx|x=0=1/e-1,故切线方程为y-1=(1/e-1)x,或y=(1/e-1)x+1.
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