z=f(xy^2,x^2y)的二阶偏导数 z^2⼀xy

2025-01-21 14:06:49
推荐回答(2个)
回答1:

Z = F(u,v) u=xy^2 v=x^2y
Z'x = F'u u'x + F'v v'x
= y^2F'u + 2xyF'v
Z''xy = 2yF'u+y^2(F''uu u'y+F''uv v'y)
= 2yF'u + y^2(2xyF''uu + x^2F''uv)
= 2yF'u + xy^2 (2y F''uu + xF''uv)

回答2:

等式两边分别求偏导,求两次即为结果