BBMP1103 - Sept 2011 exam workshop - part 6

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Prepared by Dr. Richard Ng

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BBMP1103 - Sept 2011 exam workshop - part 6

  1. 1. BBMP 1103 Mathematic ManagementExam Preparation Workshop Sept 2011 Part 6 - Partial Differentiation Presented By: Dr Richard Ng 26 Nov 2011 2ptg – 4ptg
  2. 2. 6. Focus on Partial Differentiation Question: 14 (May 2010) Solve the following questions using partial differentiation: a) Given a function f ( x, y) 5x 3 4 x 2 y 3 3 y 2 Find i) f x ( x, y ) iv) f yy ( x, y) ii) f y ( x, y ) v) f yx ( x, y) iii) f xx ( x, y) vi) f xy ( x, y)Prepared by Dr Richard Ng (2011) Page 2
  3. 3. Suggested Answers: f ( x, y) 5x 3 4 x 2 y 3 3y 2 i) f x 15x 2 (4 y 3 )[2 x] 15x 2 8xy3 ii) f y ( 4x 2 )[3 y 2 ] 6 y 12x 2 y 2 6 y iii) f x 15x 2 8xy 3 f xx 30x (8 y 3 )[1] f xx 30x 8 y 3Prepared by Dr Richard Ng (2011) Page 3
  4. 4. iv) fy 12x 2 y 2 6 y f yy ( 12x 2 )[2 y] 6 f yy 24x 2 y 6 v) fy 12x 2 y 2 6 y f yx ( 12y 2 )[2x] f yx 24xy 2Prepared by Dr Richard Ng (2011) Page 4
  5. 5. vi) fx 15x 2 8xy 3 f xy ( 8x)[3 y 2 ] f xy 24xy 2Prepared by Dr Richard Ng (2011) Page 5
  6. 6. End ofPart 6

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