设函数y=y(x)由方程ex+y+cos(xy)=0确定，则dy/dx=________．

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问题设函数y=y(x)由方程e^x+y+cos(xy)=0确定，则dy/dx=________．

选项

答案[ysin(xy)-e^x+y]/[e^x+y-xsin(xy)]

解析方程两边对x求导，得e^x+y(1+dy/dx)-sin(xy)(y+xdy/dx)=0，解得dy/dx=[ysin(xy)-e^x+y]/[e^x+y-xsin(xy)]．

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考研数学二

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