BBMP 1103Mathematic Management

Exam Preparation Workshop Sept 2011Part 6 - Partial Differentiation

Presented By: Dr Richard Ng

26 Nov 20112ptg – 4ptg

Prepared by Dr Richard Ng (2011) Page 2

Question: 14 (May 2010)

Solve the following questions using partial differentiation:

a) Given a function 2323 345),( yyxxyxf

Find i) ),( yxf x

ii) ),( yxf y

iii) ),( yxf xx

iv) ),( yxf yy

v) ),( yxf yx

vi) ),( yxf xy

6. Focus on Partial Differentiation

Prepared by Dr Richard Ng (2011) Page 3

Suggested Answers:

223 345),( 3 yyxxyxf

i) ]2)[4(15 32 xyxf x 32 815 xyx

ii) yyxf y 6]3)[4( 22

yyx 612 22

iii) 32 815 xyxf x

]1)[8(30 3yxf xx

3830 yxf xx

iv) yyxf y 612 22

6]2)[12( 2 yxf yy

624 2 yxf yy

v) yyxf y 612 22

]2)[12( 2 xyf yx

224xyf yx

Prepared by Dr Richard Ng (2011) Page 4

vi)32 815 xyxf x

]3)[8( 2yxf xy

224xyf xy

Prepared by Dr Richard Ng (2011) Page 5

End ofPart 6