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e^xy=x²+y²+1确定，则dy/dx=________．

选项

答案(2x-ye^xy)/(xe^xy-2y)【解析】e^xy=x²+y²+1两边对x求导得e^xy·(y+xdy/dx)=2x+2ydy/dx，解得dy/dx=(2x-ye^xy)/(xe^xy-2y)．

解析

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考研数学三

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