多元函数微分学及其应用.pdf

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1、精品资料欢迎下载第九章多元函数微分学及其应用第一节多元函数的基本概念1、求下列各函数的定义域，并作出其草图.(1)2211yxz；解:定义域11,11),(yxyxD,图略(2)1ln(4222yxyxz；解:由11010422222yxyxyx得:定义域xyyxyxD4,10),(222,图略(3)）（12arcsin22yxz解:由112122yx得:定义域22),(22yxyxD,图略设22),(yxxyyxf，求),(yxf解:令sxytyx,得：stsystx11代入得sststf1)1(),(2故yyxyxf1)1(),(23、求下列极限：(1)32210)(1limyxexyxy

2、x；解:(直接代入)原式=210101(2)11)(cos1lim2200yxxyyx；-第 1 页，共 19 页精品p d f 资料 可编辑资料-精品资料欢迎下载解:原式=1)11(2lim2222200yxyxxyyx(3)yyxy)(yxy102x1)sin(lim；解:原式=210221sinlimexy)(xy(xy)xxxyyx4、判断下列极限是否存在，若存在，求出极限值(1)yyxyx200lim；解:当0 x时，令2kxy，则kkkxkxxyyxkxyxyx1limlim22202002，其值与k有关，故极限不存在(2)2265limyxyxyx；解:当,yx时，有065656

3、5022222222yyxxyxyyxxyxyx，故065lim22yxyxyx5、设yxyxyxf),(，求),(limlim00yxfyx和),(limlim00yxfxy试问：极限),(lim00yxfyx是否存在？为什么？解:1),(limlim00yxfyx，1),(limlim00yxfxy极限),(lim00yxfyx不存在，因为当0 x时，令kxy，其值与k有关6、研究函数0,00,1),(2222yxyxyxf的连续性（在哪些点连续，哪些点不连续）解:),f(f(x,y)yx0001lim00，故函数在)0,0(处不连续，其它处均连续-第 2 页，共 19 页精品p d f

4、资料 可编辑资料-文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G

5、8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC

6、8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G

7、8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC

8、8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G

9、8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC

10、8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1精品资料欢迎下载第二节偏导数填空题：(1)yxff,在),(00yx处均存在是),(yxf在该点连续的既非充分也非必要条件；(2)曲线1122xyxz在点)3,1,1(处的切线与y轴正向所成的角是6；(3)设xyzln，则xzx1，yzy1；(4)设xyzef(x,y,z)，则),(fx1000，),(fy1000，),(f100z12求下

11、列函数的一阶偏导数：(1)yxxyz；解:22y)(xyxz，22y)(xxyz(2)xxy)(z1解:xyxyxy)(xy)(xzx11ln1，121xxy)(xyz(3)zyxu；解:1zzyxyxu，xxzyyuzyzln1，xxyyzuzyzlnln3求下列函数的二阶偏导数：(1)y)(xxzln解:yxxy)(xxzln，yxxyz，2222y)(xyxxz，22y)(xyyxz，222y)(xxyz，22y)(xyxyz(2)yxzarcsin；解:221xyxz，22xyyxyz，-第 3 页，共 19 页精品p d f 资料 可编辑资料-文档编码:CP6S8G8A2J8 HF3

12、A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1

13、文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3

14、A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1

15、文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3

16、A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1

17、文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3

18、A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1精品资料欢迎下载232222)xx(yxz，23222)xy(yyxz，23222122222)xx(y)x(yyxyz，12322221222)x(yx)x(yyxyz4 设函数,yx,yx,yxyf(x,y)0001cos222222判断其在点),(00处的连续性和偏导数是否存在解:1）),f(yxyf(x,y)yxyx0001coslimlim220000故函数在点),(00处连续；2）x)

19、,f()x,f(),(fxx0000lim000000lim0 xxy),f(y),f(),(fyy0000lim000yyyy01coslim20201coslimyy，极限不存在，故此点处关于y的偏导数不存在-第 4 页，共 19 页精品p d f 资料 可编辑资料-文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码

20、:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5

21、Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码

22、:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5

23、Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码

24、:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5

25、Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1精品资料欢迎下载第三节全微分填空选择题：(1)二 元 函 数f(x,y)z在 点),(y

26、x处 可 微 的 充 分 必 要 条 件 是0lim0dzz，其中zf(x,y)yx,yxf,dz为表达式(x,y)xf(x,y)xfyx,22yx(2)在点),(yx处),(yxdf存在的充分条件为CAf的全部二阶偏导数均存在；Bf连续；Cf的全部一阶偏导数均连续；Df连续且yxff,均存在2求函数xyz当2x，1y，1.0 x，2.0y时的全增量和全微分解:320128012.z30202101.).(.yyzxxzdz3求下列函数的全微分：(1)23yxz解:223yxxz，yxyz32ydyxdxyxdyyzdxxzdz32223(2)yxz解:xyxz21，2yxyyzdyyxydx

27、xydyyzdxxzdz221(3)ln(222zyxu解:2222zyxxxu，2222zyxyyu，2222zyxzzu-第 5 页，共 19 页精品p d f 资料 可编辑资料-文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6

28、S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5

29、 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6

30、S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5

31、 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6

32、S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5

33、 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1精品资料欢迎下载dzzyxzdyzyxydxzyxxdu2222222222224讨论函数xyz在点)0,0(处的可导性与可微性解:000lim000 xxxzx),(,000

34、lim000yyyzx),(,故函数xyz在点)0,0(处的偏导数存在；但2200limlimyxxydzz，其中22yx易 知 当x,y沿 直 线xy趋 于)0,0(时 此 极 限 不 存 在。故 函 数xyz在点)0,0(处不可微-第 6 页，共 19 页精品p d f 资料 可编辑资料-文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P

35、7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A

36、2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P

37、7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A

38、2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P

39、7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A

40、2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1精品资料欢迎下载第四节多元复合函数的求导法则求下列函数的偏导数或全

41、导数：(1)22yxz，34,3tytx解:dtdz=dtdyyzdtdxxz=)ytx(yx3221231=)t(662486t16t9t1(2)22xyf(v),vyz，其中f可导解:xzvf xxvvf2yzvfyyvvf211(3)yxez，)x(y，其中可导解:dxdz=dxdyyzxz=(x)xeeyy(4)设yxvyxuvuz,2,32，求yzxz,解:xz22332vuuvxvvzxuuzyz22334vuuvyvvzyuuz(5)wvuz32，13123t,wtv,tu解:dtdz=322223394vuwtvuwuv2求下列函数的偏导数：(1)(xy),yf(xzsin32

42、，其中f可导，求xz，yz解:xz21cos2f(xy)yf xyz212cos3f(xy)xfy(2)(yz)xyef(xuxsin，其中f可导，求xu，yu，zu解:xuf(yz)ye(xsin1，-第 7 页，共 19 页精品p d f 资料 可编辑资料-文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S

43、8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5

44、ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S

45、8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5

46、ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S

47、8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5

48、ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1精品资料欢迎下载yu=f(yz)xze(xcos，zu=f(yz)xycos(3)设yxef(u,

49、x,y),uz，其中f二阶可导，求xz，yxz2解:xz21ffey，yxz2=2321131121ffxefefxefeyyyy(4)设),(22yxxyfzf具有二阶连续偏导数，求22xz，yxz2，22yz解:xz2122fxyfy，yz=2212fxfxy22xz22221231142442fyxfxyfyf yyxz2=22312221132125222fyxfyxfxyfxf y22yz=22412311221442fxfyxfyxfx3已知函数f，g可导，验证at)g(xat)f(xu满足22222xuatu证明：g-afatu，gafatu2222，gfxu，gfxu22，故2

50、2222xuatu-第 8 页，共 19 页精品p d f 资料 可编辑资料-文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A3W5Z3Y5 ZC8P7W4I1N1文档编码:CP6S8G8A2J8 HF3A