数学分析,高等数学,第八题怎么做呀

2025-05-07 03:17:17
推荐回答(1个)
回答(1):

x+y+z+xyz = 0,
两边对 x 求偏导,得 1 + z' + yz + xzz' = 0,
z' = -(1+yz)/(1+xz)
f = e^x y z^2
f' = ye^x z^2 + ye^x 2zz'
= ye^x z^2 - 2yze^x (1+yz)/(1+xz)