Question

高等数学多元函数

Answer 1

z = f(u, v), u = x+y^2, v = sin(xy), 用 <> 表示下标。
z'<x> = f'<u>u'<x> + f'<v>v'<x> = f'<u> + ycos(xy)f'<v>
z''<xx> = f''<uu>u'<x> + f''<uv>v'<x>
- y^2sin(xy)f'<v> + ycos(xy)[f''<vu>u'<x> + f''<vv>v'<x>]
= f''<uu> + ycos(xy)f''<uv>
- y^2sin(xy)f'<v> + ycos(xy)[f''<vu> + ycos(xy)f''<vv>]
= f''<uu> + 2ycos(xy)f''<uv> +[ycos(xy)]^2 f''<vv> - y^2sin(xy)f'<v>
选第 2 行答案。