11Breview1sol

11Breview1sol - econ 11b ucsc ams 11b Review Questions 1...

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Unformatted text preview: econ 11b ucsc ams 11b Review Questions 1 Solutions 1. Compute the indicated partial derivatives of the functions below. a. z = 3 x 2 + 4 xy- 5 y 2- 4 x + 7 y- 2 , z x = 6 x + 4 y- 4 z y = 4 x- 10 y + 7 b. F ( u,v,w ) = 60 u 2 / 3 v 1 / 6 w 1 / 2 F u = 40 u- 1 / 3 v 1 / 6 w 1 / 2 2 F wu = 20 u- 1 / 3 v 1 / 6 w- 1 / 2 c. w = x 2 z ln( y 2 + z 3 ) w x = 2 xz ln( y 2 + z 3 ) w y = 2 x 2 yz y 2 + z 3 w xx = 2 z ln( y 2 + z 3 ) w yz = 2 x 2 y ( y 2 + z 3 )- 6 x 2 yz 3 ( y 2 + z 3 ) 2 = 2 x 2 ( y 3- 2 yz 3 ) ( y 2 + z 3 ) 2 . w xyz = 4 x ( y 3- 2 yz 3 ) ( y 2 + z 3 ) 2 , since w xyz = w yzx . d. f ( x,y,z ) = 2 x 3 yz 2- 3 xy 3 z + 5 x 2 y 2- 7 yz 5 + 11 x- 1; f x = 6 x 2 yz 2- 3 y 3 z + 10 xy 2 + 11 . f y = 2 x 3 z 2- 9 xy 2 z + 10 x 2 y- 7 z 5 . f zx = f xz = 12 x 2 yz- 3 y 3 . e. q ( u,v ) = u 2 v- 3 uv 3 2 u + 3 v ; q u = (2 uv- 3 v 3 )(2 u + 3 v )- 2( u 2 v- 3 uv 3 ) (2 u + 3 v ) 2 = 2 u 2 v + 6 uv 2- 9 v 4 (2 u + 3 v ) 2 ....
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This note was uploaded on 09/16/2011 for the course ECON 11B taught by Professor Binici during the Spring '08 term at UCSC.

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11Breview1sol - econ 11b ucsc ams 11b Review Questions 1...

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