第九章--多元函數(shù)微分學(xué)及應(yīng)用

1、1第九章第九章多元函數(shù)微分學(xué)及應(yīng)用多元函數(shù)微分學(xué)及應(yīng)用一.設(shè)fg為連續(xù)可微函數(shù)求.)()(xyxgvxyxfu???，xvxu?????解..所以yffxu21????)1(ygxv????)()1(21yffgyvvxu????????二.設(shè)其中?為可微函數(shù)求.??????????yzyzx?22yz??解.原式兩邊對(duì)y求導(dǎo)..所以22yzyyzyzyyzyzz?????????????????????????????????????

2、?????????????????yzyyzyzzyzyyz2???三.設(shè).xuzxttxyzyxfu?????，求，，又)()()(??解.由上述表達(dá)式可知xz為自變量所以??xtyxyxxtxyxyxfffffxyffxu??????????????????四.求下列方程所確定函數(shù)的全微分:1.dzxzzyyxf，求0)(????2..dzyzxzfz，求，)(??解.1.所以0)1(321????????xzfxzff3231ff

3、ffxz??????所以0)1(231????????yzfyzff3221ffffyz??????所以)()(322131ffdyffdxffdyyzdxxzdz????????????3七.設(shè)確定求.?????????????00)()(322zzyxzzyxxzzxyy，由，dxdzdxdy，解.以上兩式對(duì)x求導(dǎo)得到關(guān)于的方程組dxdzdxdy，???????????????0321021dxdzzdxdzdxdyydxdzzdx

4、dzdxdy???????????????1)31(21)21(dxdzzdxdyydxdzzdxdy由克萊姆法則解得yzyzzzdxdy42313222?????yzyzydxdz4231122?????八.設(shè)22222222)()(yzyyxzxyxzxxyxyxfz???????????，求?解.)()()())(())(()(222xyxyxyfxyxyfxyxyxyxyxfxyfxz????????????)()(2)()()

5、(423422222xyxyxyxyxyfxyxyfxyxyfxyxz??????????=242332??xyxyfxy??)()(1)()(1)(13222xyxyxyxxyfxyxyfxxyfxyxz??????????1322??xyxfxy????)(1)(xyxxyfyz?????11222?xfxyz????于是=22222222yzyyxzxyxzx?????????2222??xyxyfxy??222222??xyxy