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+y4)+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+uv.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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