2. 考研
  3. 设y=y(x)由方程ex+y+cos(xy)=sin3x+2确定，则dy/dx｜x=0=________．

设y=y(x)由方程ex+y+cos(xy)=sin3x+2确定，则dy/dx｜x=0=________．

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问题 设y=y(x)由方程ex+y+cos(xy)=sin3x+2确定，则dy/dx｜x=0=________．
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答案2
解析 当x=0时，由ex+y+cos(xy)=sin3x+2得y=0；ex+y+cos(xy)=sin3x+2两边对x求导得ex+y·(1+dy/dx)-sinxy·(y+xdy/dx)=3cos3x，代入得dy/dx｜x=0=2．
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考研数学三

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