设z=(3x2+y2)xy,则等于( )

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问题 设z=(3x2+y2)xy,则等于(    )

选项 A、xy·(3x2+y2)xy-1
B、(3x2+y2)xy·ln(3x2+y2)
C、y·(3x2+y2)xy[(3x2+y2)ln(3x2+y2)+6x2]
D、y·(3x2+y2)xy-1[(3x2+y2)ln(3x2+y2)+6x2]

答案D

解析 因z=(3x2+y2)xy可看作是z=uv,u=3x2+y2,v=xy复合而成,

=v·uv-1·6x+u2·lnu·y
=xy·(3x2+y2)xy-1·6x+(3x2+y2)xy·ln(3x2+y2)·y
=y·(3x2+y2)xy-1·[(3x2+y2)ln(3x2+y2)+6x2].
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