设y=y(x)由exy=x2+y2+1确定,则dy/dx=________.

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问题 设y=y(x)由exy=x2+y2+1确定,则dy/dx=________.

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答案(2x-yexy)/(xexy-2y)

解析 exy=x2+y2+1两边对x求导得exy(y+xdy/dx)=2x+2ydy/dx,解得dy/dx=(2x-yexy)/(xexy-2y).
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