BBMP 1103Mathematic Management

Exam Preparation Workshop Sept 2011Part 2 - Differentiation

Presented By: Dr Richard Ng

26 Nov 20112ptg – 4ptg

Prepared by Dr Richard Ng (2011) Page 2

Question: 4 (May 2010)

Differentiate the following functions:

a) 35)( xxf

b) )12()( 363

2

xxxxf

c) )]24)(3[()( 2 xxxxf

d)2

23 735)(

x

xxxp

Find )(' xf and )('' xf 3 marks

Find )(' xf 3 marks

Find )('' xf 4 marks

Find )('' xp 3 marks

2. Focus on Differentiation

a) 35)( xxf

23

5)( xxf

21

)5(2

3' xf

2

1

2

15

2

1''

xf

2

1

4

15''

xf

Suggested Answers:

Prepared by Dr Richard Ng (2011) Page 3

21

2

15' xf

21

2

15' xf

b) )12()( 363

2

xxxxf

3

13625

3

2)12(66'

3

2

xxxxxxf

c) )24(3)( 2 xxxxf

1)24(283' 2 xxxxf

)28(1)28(83'' xxxf

)28()28(248 xxx

2824 x

Prepared by Dr Richard Ng (2011) Page 4

d) 2

23 735)(

x

xxxp

22

2

2

3 735

xx

x

x

x

2735 xx

37)2(5' xp

3145 x

442'' xp

Prepared by Dr Richard Ng (2011) Page 5

Question: 5 (January 2011)

a) 630044212 23 xxxy

30088436 2 xxdx

dy

b)2

2

1 xx

y

32 xdx

dy

c) xxxx

y5

1

15

1

15

3 55

5

1

3

1

5

1

15

5 44 xxdx

dy

d) 25

13

x

xy

2)25(

]5)[13(]3)[25(

x

xx

dx

dy

2)25(

)515(615

x

xx

2)25(

11

x

e)1

122

2

x

xxy

)1(

)1(

)1)(1(

)1)(1(

1

122

2

x

x

xx

xx

x

xx

2)1(

]1)[1(]1)[1(

x

xx

dx

dy

2)1(

11

x

xx

2)1(

2

x

Question: 6 (January 2010)

End ofPart 2