填空题
设f(x,y)=sin(xy
2
)，则df(x,y)= 1．
【正确答案】
【答案解析】y
2
cos(xy
2
)dx+2xycos(xy
2
)dy
[考点] 本题考查了二元函数的全微分的知识点．
[解析] df(x,y)=cos(xy 2 )d(xy 2 )
=cos(xy 2 )(y 2 dx+2xydy)
=y 2 cos(xy 2 )dx+2xycos(xy 2 )dy．
注：本题也可先求出
[解析] df(x,y)=cos(xy 2 )d(xy 2 )
=cos(xy 2 )(y 2 dx+2xydy)
=y 2 cos(xy 2 )dx+2xycos(xy 2 )dy．
注：本题也可先求出