经济数学基础讲义第7章多元函数微分学

.专业..第4章多元函数微分学yf(x)精品文档放心下载zf(x,y)uf(x,y,z)谢谢阅读例1r,hv感谢阅读.r和hv.精品文档放心下载D(r,h)r0.例2t(x,y)zzz(x,y,t).感谢阅读例3t(x,y,z)u是x,y,z,t谢谢阅读谢谢阅读uu(x,y,z,t)感谢阅读例4za2x2y2感谢阅读axy0D(x,y)xya精品文档放心下载222222例5求zy)yy0xy

0D(x,y)yy0感谢阅读——zf(x,y)(x,y00)x.word完美格式..专业..,y)f(xx,y)fyy000(xx000xz(x)y,y或fx00x00x(x,y)00)f(x,yy)f(x00yy0,y00）zxsin3y2zyf(x,y)3x2cosyzy(1,0)3fy3x2cos(1,0)xy对x感谢阅读y.z对y精品文档放心下载.yf(x)在x.x00)(x,yzf(x,y)在(x,y0000).zf(x,y)称zz

xyxyzz

xyzf(x,y)(x,y).感谢阅读例1:求zf(x,y)xsin3yx.谢谢阅读2zzy2xsin将x，x2xsin(1,0)0(1,0).word完美格式..专业..例求zx2yyx.z(2xyy)21)2，y2xx2x(1,1)(1,1)(1,1)谢谢阅读(1,1)精品文档放心下载dzdx2dy设zf(u,v)uu(x,y)，vv(x,y)谢谢阅读zzuzvzzuzv，感谢阅读xuxvx感谢阅读uyvy例zesin(xy).uxy，vxyzeusinv谢谢阅读zzuzv(eusinv)y(eucosv)1sin(xy)ecos(xy)

xuxvx感谢阅读zeusinv，uxy，vxy精品文档放心下载zzuzv

(eusinv)x(eucosv)1xexysin(xy)exycos(xy)精品文档放心下载yuyvyz(e)y))y)exxxzyxexysin(xy)exycos(xy)zz例zf(xy,xy)，,．求xy设uxy,vxy则zf(u,v)，yesin(xy)ecos(xxyxyy)zzuzvfyf1yffuvuvxux

vxzzuzvfxf1xffyuyvyuvuv谢谢阅读.word完美格式..专业..例3zf(x,xy)2:设ux,vxy,则zf(u,v)，2zzuzvxuxvxf1fyuv2fy2xyf2fuvv例4zf(3x,sinx)，求2．ff(u,v)，u3x2,vsinx谢谢阅读而zu,vx谢谢阅读谢谢阅读zzf6xfcosxuvuv例5zf(xy)，求23zz,．xyfzx,y精品文档放心下载zf(u),uxy，23zuzu3ff3xff2xy，2y2yyxx例6F(x,y)xya0(y0)精品文档放心下载222yy(x)ax22dy2xxdx2a2x2yxya0，xy(x)a0222222感谢阅读d:2x2yy0，yxy例7yy(x)xyye20y(x)谢谢阅读:y(x)y(x)感谢阅读xlny(x)y(x)exy(x)20dy:yxye

yxyyexy(y)0ylnyy3exy

y:y，

xxyxy2exy感谢阅读.word完美格式..专业..)是f(x,y)(x,y)(x,y)f(x,y)f(x,y)(x,y000000f(x),y00谢谢阅读yf(x)在f)

xx(x0000zf(x,y)在(x)(x,y),y0000(x(x))0，f,y,y0

fx00y00若zf(x,y)Dzf(x,y)在D感谢阅读(x0若zf(x,y)在DD(x,y00,y)0)zf(x,y)点谢谢阅读例2V感谢阅读x,yVxyS2xVVVV2y22xyxyyx.word完美格式..专业..0，Sx0yS2yxxy2Vxy33xy232、、332S=xy+xh+yh精品文档放心下载xyh=Vf(x,y,z)在条件(x,y,z)0感谢阅读Ff(x,y,z)(x,y,z)谢谢阅读求Ff(x,y,z)(x,y,z)精品文档放心下载FFFxyzF(x,y,z)0：Sxy2xh2yhxyhV感谢阅读令Lxy2xh2yh(xyhV)感谢阅读LxLyLhy2hyhx2hxh