Implicit Differentiation - ‘l.’ IMPLICIT DIFFERENTmen)...

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Unformatted text preview: ‘l.’ IMPLICIT DIFFERENTmen) HOTNOTION : COHPBRE '7. 3 3 I. 7C "y = 3 “"7” y: «Ix'u3 2, ‘0. a. x +y =1 won-I y:1/l-xl 3 3 3. x +y = 3x7 mm ,2 y I; amen mummy )1 as owewexmcmy as a FUNCTION OF x as 0 FUNCTIoN 0? X. . 3 Non? mar :15 Easy To wnpuTE y' omeeny Peon y = 1/x‘-3 = .1. a ’ O 7' = (cx‘-3)’) = j-cxfis) ’c-‘w ___£2.‘__. :1 3 he‘- 3) 3 . O But also NOTICE 17:01“ you CAN GET y’ DIRECTLY FRon xl- y3= 3 BY REGDRDING y as sons "awkmomw " FUNCTION 0? x , mFFERENTmnNG 8077’ mass BM) 03:»: WE cum» RULE 3 cx"- V3), = (3) ' a") '— cy')’ = 0 4x - 3’27: = o (CHAINRDLE ! ) THE “ y ” fiPPEfiRS HERE Because we maven-T .soLvED ,3.” = 3 F08 y. J- IF wE mo sows FOR y wE‘D car y : axis” mun, 5085711077106 Tim ’ THE mo mus wees PM y ’ wow BE THE $1905 , sonETmES Haw»; rue y no we sxmsssmn Fox y’ w A cool: mmc : sxmma : FIND we “we OF THE mmsem'r LINE Tb THE cmcLE 112+)!" a l m m Mammy POINT («J») c «an: L #0 ) Nora : pom-r KNow «mama-m (4,5) :5 an) me Top HALF cy m': x‘ )02 ms 801100 mam (y: “(h—:7). 2. 3 m0 y'ns we ow Fan x ~y =3: ’ I 0(5)”) % I cx‘)’uy'-J’ = 0 X y, g - 7- (y¢0) was, THE 51.095 01 (4.5) IS 9;. b y’ugb) =~ " THIS PROCEDURE Fox moms y ’ :s EVEN nape USEFUL wits» IT'S smmy lnPosswLE‘ TD SOLVE FOR )1 EXPLICITLY‘ E. 6., FOR x3 + y3 = Bxy cx3+y3)’= (3xy)’ an)’+cy3)’ = 300’), 3:12 +3y‘y’ = 3 (Xy’+7‘¥”) x" + y‘Y' " ‘7'4'7 yty’-xy’ '3 y-X” l. I .x‘ ()1 fly 3 7 '- y-X y, a Iy‘nx MORE EXHHPLES : I. THE 6MP» 0F X3”!3 '-‘ 3):)! 1s amen me Fouun 3f 0550917755 nun LOOKS Lute Tm: : Y ($.35) ca " roman" as n LEBF am 3. mm. x osscmmss IS sane mam» cur ) 3 .3. rue SLOPE 0F m5 m~as~r LINE or t a“ . a. ) vs 2.. .3. " y’<%a%)= ‘ f‘,’ (id-s: u .2, FIND y’ IF y IS GWEN arm.er 37 x": Jil- Hcscy LX‘)’ = (—1” )’ Hcscy ax : cHcscy)(cacSczy)y’)-(coiy)((-c5czcol'y)y’) (Huey); z 3 2 Ax : cucsc z-escy + cscyco” ’12)! I L H cscy)‘ z z ax z -cscy(csc7+cscy—cofy)y’ ( Hcscyr -csc ’ 2.x a Y (“5‘ Y * ” Z 351180833: (,H any)‘ csa‘y.¢d'7= I 1X : (. cscy )y’ H cscy $0 I 3 - W - y cscy .. 4x(swy +1) I z. 7 3 ' 7i 1 l 50 ' x1- I y‘(ax)— K (3!)! ) )’ ' = Wm“ C“ 7:) 3 ' oy‘)‘ ‘- _ Axyz-ax‘y (- 3‘1) axy‘+1xq(§) . ~ II'll-l“..._._...._-—-—————-L--—'yV -" g. 1;: 13+ .1)!" ...
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This note was uploaded on 10/23/2011 for the course MATHEMATIC 221 taught by Professor Staff during the Fall '09 term at East West University, Chicago.

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Implicit Differentiation - ‘l.’ IMPLICIT DIFFERENTmen)...

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