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=_____________.

admin2019-11-25  18

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-1g’1+yxy-1lnxg’1+yx2y-1lnxg”11+2y2xy-1g”12+2xy+1lnxg”21+4xyg”22

解析 由z=xf(x+y)+g(xy,x2+y2),得
=f(x+y)+xf’(x+y)+yxy-1 g’1(xy,x2+y2)+2xg’2(xy,x2+y2),
=f’+xf”+xy-1g’1+yxy-1lnxg’1+yx2y-1lnxg”11+2y2xy-1g”12+2xy+1lnxg”21+4xyg”22
转载请注明原文地址:https://jikaoti.com/ti/T8iRFFFM
0

最新回复(0)