Z = F(u,v) u=xy^2 v=x^2yZ'x = F'u u'x + F'v v'x = y^2F'u + 2xyF'vZ''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)
等式两边分别求偏导,求两次即为结果