Transcript
Page 1: 11X1 T17 06 derivative times function (2010)

dxxfxf n

Page 2: 11X1 T17 06 derivative times function (2010)

cnxfdxxfxf

nn

1

1

dxxfxf n

Page 3: 11X1 T17 06 derivative times function (2010)

cnxfdxxfxf

nn

1

1

31 Find a) e.g. xdxdi

dxxfxf n

Page 4: 11X1 T17 06 derivative times function (2010)

cnxfdxxfxf

nn

1

1

31 Find a) e.g. xdxdi

3

2

221

33

123

31211

xx

xxxdxd

dxxfxf n

Page 5: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

Page 6: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

Page 7: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

Page 8: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

Page 9: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

Page 10: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

Page 11: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

cxx 22 2231

Page 12: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

cxx 22 2231

OR dxxx 22

Page 13: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

cxx 22 2231

OR dxxx 22 22 xu

Page 14: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

cxx 22 2231

OR dxxx 22 22 xu

xdxdu

xdxdu

2

2

Page 15: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

cxx 22 2231

OR dxxx 22 22 xu

xdxdu

xdxdu

2

2

u

Page 16: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

cxx 22 2231

OR dxxx 22 22 xu

xdxdu

xdxdu

2

2

udu

21

Page 17: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

cxx 22 2231

OR dxxx 22 22 xu

xdxdu

xdxdu

2

2

udu

21

duu 21

21

Page 18: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

cxx 22 2231

OR dxxx 22 22 xu

xdxdu

xdxdu

2

2

udu

21

duu 21

21

cu 23

32

21

Page 19: 11X1 T17 06 derivative times function (2010)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

cx 23

2232

21

cxx 22 2231

OR dxxx 22 22 xu

xdxdu

xdxdu

2

2

udu

21

duu 21

21

cu 23

32

21

cxx 22 2231

Page 20: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

Page 21: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

Page 22: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

Page 23: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

Page 24: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

81

21

11

61

22

Page 25: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

81

21

11

61

22

OR

1

033

2

2dx

xx

Page 26: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

81

21

11

61

22

OR

1

033

2

2dx

xx

dxxduxu

2

3

32

Page 27: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

81

21

11

61

22

OR

1

033

2

2dx

xx

dxxduxu

2

3

32

1,12,0

uxux

Page 28: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

81

21

11

61

22

OR

1

033

2

2dx

xx

dxxduxu

2

3

32

1,12,0

uxux

1

2

3

31 duu

Page 29: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

81

21

11

61

22

OR

1

033

2

2dx

xx

dxxduxu

2

3

32

1,12,0

uxux

1

2

3

31 duu

12

2

61

u

Page 30: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

81

21

11

61

22

OR

1

033

2

2dx

xx

dxxduxu

2

3

32

1,12,0

uxux

1

2

3

31 duu

12

2

61

u

81

21

11

61

22

Page 31: 11X1 T17 06 derivative times function (2010)

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

81

21

11

61

22

Exercise 11H; 1, 3, 5, 7ace etc, 8bdf,9 11*

OR

1

033

2

2dx

xx

dxxduxu

2

3

32

1,12,0

uxux

1

2

3

31 duu

12

2

61

u

81

21

11

61

22


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