设z=xf(x+y)+g(xy,x2+y2),其中f,g分别二阶连续可导和二阶连续可偏导,则=______.

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问题 设z=xf(x+y)+g(xy,x2+y2),其中f,g分别二阶连续可导和二阶连续可偏导,则=______.

选项

答案f’+xf’’+xy-1g1’+yxy-1lnxg1’+yx2y-1lnxg11’’+2y2xy-1g12’’+2xy+1lnxg21’’+4xyg22’’.

解析 由z=xf(x+y)+g(xy,x2+y2),得
=f(x+y)+xf’(x+y)+yxy-1g1’(xy,x2+y2)+2xg2’(xy,x2+y2)
=f’+xf’’+xy-1g1’+yxy-1lnxg1’+yx2y-1lnxg11’’+2y2xy-1g12’’+2xy+1lnxg21’’+4xyg22’’.
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