Answer

问题及解答

w=f(x+y+z,xyz), f 具有二阶连续偏导数, 求 2wxz.

Posted by haifeng on 2023-03-29 13:07:13 last update 2023-03-29 13:07:13 | Edit | Answers (1)

w=f(x+y+z,xyz), f 具有二阶连续偏导数, 求 2wxz.

 

1

Posted by haifeng on 2023-03-29 13:14:01

wx=f11+f2yz

2wxz=z(wx)=z(f1+f2yz)=(f111+f12xy)+(f211+f22xy)yz+f2y=f11+xyf12+yzf21+xy2zf22+yf2

又由题设, f 的二阶导数连续, 故 f12=f21. 于是上式可化简为

f11+(x+z)yf12+xy2zf22+yf2