經(jīng)濟(jì)數(shù)學(xué)基礎(chǔ)講義第7章多元函數(shù)微分學(xué)

.專業(yè)..第4章多元函數(shù)微分學(xué)yf(x)精品文檔放心下載zf(x,y)uf(x,y,z)謝謝閱讀例1r,hv感謝閱讀.r和hv.精品文檔放心下載D(r,h)r0.例2t(x,y)zzz(x,y,t).感謝閱讀例3t(x,y,z)u是x,y,z,t謝謝閱讀謝謝閱讀uu(x,y,z,t)感謝閱讀例4za2x2y2感謝閱讀axy0D(x,y)xya精品文檔放心下載222222例5求zy)yy0xy

0D(x,y)yy0感謝閱讀——zf(x,y)(x,y00)x.word完美格式..專業(yè)..,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對(duì)x感謝閱讀y.z對(duì)y精品文檔放心下載.yf(x)在x.x00)(x,yzf(x,y)在(x,y0000).zf(x,y)稱zz

xyxyzz

xyzf(x,y)(x,y).感謝閱讀例1:求zf(x,y)xsin3yx.謝謝閱讀2zzy2xsin將x，x2xsin(1,0)0(1,0).word完美格式..專業(yè)..例求zx2yyx.z(2xyy)21)2，y2xx2x(1,1)(1,1)(1,1)謝謝閱讀(1,1)精品文檔放心下載dzdx2dy設(shè)zf(u,v)uu(x,y)，vv(x,y)謝謝閱讀zzuzvzzuzv，感謝閱讀xuxvx感謝閱讀uyvy例zesin(xy).uxy，vxyzeusinv謝謝閱讀zzuzv(eusinv)y(eucosv)1sin(xy)ecos(xy)

xuxvx感謝閱讀zeusinv，uxy，vxy精品文檔放心下載zzuzv

(eusinv)x(eucosv)1xexysin(xy)exycos(xy)精品文檔放心下載yuyvyz(e)y))y)exxxzyxexysin(xy)exycos(xy)zz例zf(xy,xy)，,．求xy設(shè)uxy,vxy則zf(u,v)，yesin(xy)ecos(xxyxyy)zzuzvfyf1yffuvuvxux

vxzzuzvfxf1xffyuyvyuvuv謝謝閱讀.word完美格式..專業(yè)..例3zf(x,xy)2:設(shè)ux,vxy,則zf(u,v)，2zzuzvxuxvxf1fyuv2fy2xyf2fuvv例4zf(3x,sinx)，求2．ff(u,v)，u3x2,vsinx謝謝閱讀而zu,vx謝謝閱讀謝謝閱讀zzf6xfcosxuvuv例5zf(xy)，求23zz,．xyfzx,y精品文檔放心下載zf(u),uxy，23zuzu3ff3xff2xy，2y2yyxx例6F(x,y)xya0(y0)精品文檔放心下載222yy(x)ax22dy2xxdx2a2x2yxya0，xy(x)a0222222感謝閱讀d:2x2yy0，yxy例7yy(x)xyye20y(x)謝謝閱讀:y(x)y(x)感謝閱讀xlny(x)y(x)exy(x)20dy:yxye

yxyyexy(y)0ylnyy3exy

y:y，

xxyxy2exy感謝閱讀.word完美格式..專業(yè)..)是f(x,y)(x,y)(x,y)f(x,y)f(x,y)(x,y000000f(x),y00謝謝閱讀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感謝閱讀(x0若zf(x,y)在DD(x,y00,y)0)zf(x,y)點(diǎn)謝謝閱讀例2V感謝閱讀x,yVxyS2xVVVV2y22xyxyyx.word完美格式..專業(yè)..0，Sx0yS2yxxy2Vxy33xy232、、332S=xy+xh+yh精品文檔放心下載xyh=Vf(x,y,z)在條件(x,y,z)0感謝閱讀Ff(x,y,z)(x,y,z)謝謝閱讀求Ff(x,y,z)(x,y,z)精品文檔放心下載FFFxyzF(x,y,z)0：Sxy2xh2yhxyhV感謝閱讀令Lxy2xh2yh(xyhV)感謝閱讀LxLyLhy2hyhx2hxh