11 x1 t16 06 derivative times function

dxxfxf n

cnxfdxxfxf

nn

1

1

dxxfxf n

cnxfdxxfxf

nn

1

1

31 Find a) e.g. xdxdi

dxxfxf n

cnxfdxxfxf

nn

1

1

31 Find a) e.g. xdxdi

3

2

221

33

123

31211

xx

xxxdxd

dxxfxf n

dxx

x 3

2

1 find; Hence b)

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxx

x 3

2

1 find; Hence b)

dxx

xdxx

x3

2

3

2

123

32

1

cx 3132

dxxxii 22

dxxx 222 21

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

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

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

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

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

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

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

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

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

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

1

033

2

2dx

xxiii

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1

033

2

2dx

xxiii

1

033

2

23

31 dx

xx

1

0

332 2331 dxxx

1 0 23 261

x

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

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

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

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

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

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

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

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