This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Gauthier, Joseph Homework 10 Due: Nov 1 2007, 3:00 am Inst: JEGilbert 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Determine f x f y when f ( x,y ) = 2 x 2 + 2 xy 4 y 2 3 x 2 y . 1. f x f y = 6 x + 10 y 5 2. f x f y = 6 x 6 y 1 3. f x f y = 6 x 6 y 5 4. f x f y = 2 x 6 y 1 5. f x f y = 2 x + 10 y 5 6. f x f y = 2 x + 10 y 1 correct Explanation: After differentiation we see that f x = 4 x + 2 y 3 , f y = 2 x 8 y 2 . Consequently, f x f y = 2 x + 10 y 1 . keywords: partial derivative, first order par tial derivative, polynomial 002 (part 1 of 1) 10 points Determine f x when f ( x, y ) = cos(2 y x ) x sin(2 y x ) . 1. f x = cos(2 y x ) x sin(2 y x ) 2. f x = 2 sin(2 y x ) x cos(2 y x ) 3. f x = x sin(2 y x ) 4. f x = x cos(2 y x ) 5. f x = x cos(2 y x ) sin(2 y x ) 6. f x = 2 sin(2 y x ) x cos(2 y x ) 7. f x = x sin(2 y x ) 8. f x = x cos(2 y x ) correct Explanation: From the Product Rule we see that f x = sin(2 y x ) sin(2 y x )+ x cos(2 y x ) . Consequently, f x = x cos(2 y x ) . partial derivative, first order partial deriva tive, trig function, keywords: 003 (part 1 of 1) 10 points Determine f x when f ( x, y ) = ( xy 3) e xy . 1. f x = y (2 xy ) e xy 2. f x = y (2 + xy ) e xy 3. f x = y ( xy 4) e xy 4. f x = x (4 3 xy ) e xy 5. f x = y (4 xy ) e xy correct 6. f x = x (3 xy 4) e xy 7. f x = x (2 + 3 xy ) e xy 8. f x = x (2 + xy ) e xy Explanation: From the Product Rule we see that f x = ye xy y ( xy 3) e xy . Gauthier, Joseph Homework 10 Due: Nov 1 2007, 3:00 am Inst: JEGilbert 2 Consequently, f x = y (4 xy ) e xy . keywords: partial derivative, first order par tial derivative, exp function, 004 (part 1 of 1) 10 points Determine h = h ( x,y ) so that f x = h ( x,y ) ( x 2 + 5 y 2 ) 2 when f ( x,y ) = 4 x 2 y x 2 + 5 y 2 . 1. h ( x,y ) = 20 xy 3 2. h ( x,y ) = 40 xy 2 3. h ( x,y ) = 20 x 3 y 4. h ( x,y ) = 40 x 3 y 5. h ( x,y ) = 40 xy 3 correct 6. h ( x,y ) = 20 xy 2 Explanation: Differentiating with respect to x using the quotient rule we obtain...
View
Full
Document
This homework help was uploaded on 03/19/2008 for the course M 408M taught by Professor Gilbert during the Fall '07 term at University of Texas at Austin.
 Fall '07
 Gilbert

Click to edit the document details