Chapter 9.2 Partial Derivatives Oct 14, 2019 7_00_47 PM - first partial derivative of the The by treating x as a that by is denoted flxth.in f Ix

# Chapter 9.2 Partial Derivatives Oct 14, 2019 7_00_47 PM...

• Notes
• 3

This preview shows page 1 - 3 out of 3 pages.

The first partial derivative of the function 2 Hx y is obtained by treating x as a variable 4 y as a constant number that is denoted by f Ix y tx x y Lingo flxth.in flx 1 partial derivative of the function 2 FIX y is obtained by treating y as a variable 4 x as a constant h is denoted by fly f Ix y fy Ix y e tyg H iYth1 fh h Examples 1 fix y x'thly a lb 1 f 3 2 b fi 4 2 2 6 2 4xy t 9 y lat lb let 1431 d 11 21 a f 12 x 4y 1 f y 4 18 y 12121 4131 12 d 4 l t 181 2 40 3 FIX y 9 2 y u 4 y 2 f 942 2x O 18 112 fx 2 1 1812 l 112 36 f 9 2 ly Oy 18 x'y 8 y f l 4,3 181 41213 8131 840 4 fl x y ye 3 1 211 fx 4 e 3 24 3 0 12 e 3 24
f y 4 e 3 1 24 Ot 2 n f e 3 2 y S fl x yl In l It 5 3,12 I f c g 11 5 34 yy Ot S y 13 2 f y a yt I 111 5 3 y py Ot 5 3 ly 6 fl x y x ex Y h x l le 1 te I x x e Il ix y e 111 x e 12 41 te t i e 2x y ti t x FT le x e t Fy l x'y xe t x x'e Y 7 fIx y f e t2lF l3x2y 3x2yl le Y 2 e t 212 emi 216xyl 3x yle.li 6xyleMt2 3x2y2exY e t 212 e Y 1 2 Z f y e t2lfy 3x'y 3x2y oyle Yt e 2 2 e 213 2 3 2 y le x 3 2 e t 2 3 3 le e x't 2 e Y 2 t Ix y f f y f t t t f y f f xy fy f x f xx f yy 8 fl x yl 4 x'y 16 2 t 4y a f x lb f y c f xx d f yy let fxy
l I Ifl tyx q fi 4 y 2x 324 8 112 32 1 f 4 2 ly 0 4 8 2 y t 4 E fxx 8yd 32 I f y 8 2 e fx 8 1211 O 16 1 I fyx 8y 2x 10 16 1 9 f X y 5 4 y t 12 y Ax g f a 5,12 4 3 t O 9 20 3 y 9 1 f y S x ly t 36 y 10 4 y t 36,12 E 1 xx 60 2 y d fyi 10x t 72 y E f y 40 3 y 1 fyi 40 3 y 10 Suppose that the manufacturing cost of a laptop is approximated by f x y Sx't 40 y 2 Oxy 150 where x is the cost of processors h y is cost of labor Find lat f y 4,2 lb fx 3 6 c off 12,51 d oof 16,7 fy tx yl 80 y 20 x fx x y 90 20 y 1 f y 14,2 8012 2014 80 1 f x 3,6 9013 2016 150