Partial preview of the text
Download Partial differentiation (part-A) and more Summaries Mathematics in PDF only on Docsity!
Ub -; Feertial it-fere renotion. ; Single Vai alle Several Vartable - Ti Ti ae Ut po ted fOoy) © L # e@) ° £@) i 2a Kye $ Guy) ~ £ (ab) we a 2 ots, Y 2 lini and Contfnutety of functions af to variables Lintits 3 efinttion: ene G0y= ond We veod. ti (muy) > Cab) j toi of Puy) as (a, 4). approches (arb) fs by i we wart fob,’ we can make f(x,y) as close 5 1) Mud simply by Teer, Guy) close onaugyy Je (a not equal to it- Remarks ; 4 ; y h a is ‘is an 4o note hat when computing. It 4, y) = = (x14) > Cay b) “a rs ever equal ope Tn Fact, the Puriction Bi ke cteBne! a Gayo) et “™ Hitt may i exisl. While (a/b) ramp not be ‘in domain of f the points (%y) me We consider as (%y) (a)b) ae ‘ae . ‘in domain £ Ike fle yYan-y yoo L>2 2% -YoY co sationlize tea’ “comes =O? . saa Se ce a (a> (20) ax-y-+ ? alti eo ar —0)- 4 " t Lf Vot-2 , we a ar-Y ee £ SOK Ay ts (er) J ° 48 ston oh@ ) beh See : Paes WS> 83 Va 4 = —, eT (Ea \pos Te }> te 0 7l2- Ve Vy m~>0 gy L370 "OW a rea Ler} =Oy aia He Septbiar of I ay ‘o => (0,0) vy se ah rac ai - 4b 7 ae ate \s of ee “ory Fa Sh oo a een ee | continous af (e,0) 9 tt | Ik Coyy+ acovy*-0420y)} yd 120 > es [ 0 +0-0+2y] ES Yi [o 40-0 42003]. ° = cc) along yo IE [ LE # (ger) + 91° % +20) ame A>O Yor tt [ x’m + amint_1+9m] ae 120 Lo “pope hr Joe [co)’m o 3¢en') (0-0, +27C3) , dence £69) 0 = ee pe Livi) en $(any) fs Cortinous « ‘ my okey ae = ug We Hlowtng functio,,. i rae Hig continuity for q at Z gmuy origin . } e o ‘ cS ee ee ) £ (my) - aye Bs ghee Ee pe uy) = (29) ’ ee, te at - lt my) yoo : gv) 207G) E yl — 4 y+ aoe ” " GN sr mer || ae 200)] L 0 +0" lt [att 20oYy iy \eysod [a Yee hoa ory ! along Yam =0 eva ze) : ly 4 \ olr along ye mae chain sule : 3 Af *wais a -functton, of Mey rand ye Me ‘fal urselves functions of 4 te. Hf zisa composite cBve % P won ohn 4then Whe cevivalive of # with an ne 7 48 ven chain ule - ro | vespect ¢ ae RCW i) : du . au du yd du , Az Refit, at Bide + Beal #5 SE at PAs ot 2 1S a funchon of %Y--and wy thumse Ives a as Be otros OF t te iP =m Sees compo si le Lee of t Pun the devvattve of &@ with meegert te & dz. dt. da 4232. gy Ob ou ab Ex Al: nit 2 _ of 2 isa -fuction of o ayy and nuy thennselves axe. fe -tunchons of uv ve. 2 is a compostle function «| F uv then the partial clefivattives of Ee oh, nrespect a u and v are b given wae 02 . Gee Ge fr 22, dz ax, B2 ay -E dx yd dy ou | Ae ie ay Ae ae he ox vy ae & if wis a Auction of ayy, % and aye themselves ave the functions of U,v te., if wis a composite function of UV then te paréal ‘derivatives of 2 pith respect to wand V are quer by: Qw - QW au dw 24, dw az ie de OU “Oy OY 4 Be er ux cos (VexHVY), Frove that x x» Hf ' cf on age a + ty if = A cf Wee oe a Fy leb y= ati f r ur cos (¥X4+VE ) ae eg A ats Sy Gos (verve) = on Wa 4VE) (59°) = -4_(6in va 4VE)) ave , a ee ae = mo > vere wit to y ) tet ses AS nf) ary avy ) sin) + on GHW _ wey) Y a 42 ee, YE - yt) 
