12 x1 t01 02 differentiating logs (2013)

Differentiating Logarithms

Differentiating Logarithms

xfy log

Differentiating Logarithms

xfy log

xfxf

dxdy

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

xfaxf

dxdy

log

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

xfaxf

dxdy

log

e.g. (i) 53log xy

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

xfaxf

dxdy

log

e.g. (i) 53log xy

533

xdx

dy

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

xfaxf

dxdy

log

e.g. (i) 53log xy

533

xdx

dy 3log xyii

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

xfaxf

dxdy

log

e.g. (i) 53log xy

533

xdx

dy 3log xyii

3

23xx

dxdy

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

xfaxf

dxdy

log

e.g. (i) 53log xy

533

xdx

dy 3log xyii

3

23xx

dxdy

x3

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

xfaxf

dxdy

log

e.g. (i) 53log xy

533

xdx

dy 3log xyii

3

23xx

dxdy

x3

3log xy OR

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

xfaxf

dxdy

log

e.g. (i) 53log xy

533

xdx

dy 3log xyii

3

23xx

dxdy

x3

3log xy xy log3

OR

Differentiating Logarithms

xfy log

xfxf

dxdy

xfy alog

xfaxf

dxdy

log

e.g. (i) 53log xy

533

xdx

dy 3log xyii

3

23xx

dxdy

x3

3log xy xy log3

xdxdy 3

OR

(iii) xy loglog

(iii) xy loglog

xx

dxdy

log

1

(iii) xy loglog

xx

dxdy

log

1

xx log1

(iii) xy loglog

xx

dxdy

log

1

xx log1

23log xxyiv

(iii) xy loglog

xx

dxdy

log

1

xx log1

23log xxyiv

23

1213

xxxx

dxdy

(iii) xy loglog

xx

dxdy

log

1

xx log1

23log xxyiv

23

1213

xxxx

dxdy

2352

xxx

(iii) xy loglog

xx

dxdy

log

1

xx log1

23log xxyiv

23

1213

xxxx

dxdy

2352

xxx

OR 2log3log xxy

(iii) xy loglog

xx

dxdy

log

1

xx log1

23log xxyiv

23

1213

xxxx

dxdy

2352

xxx

OR 2log3log xxy

21

31

xxdxdy

(iii) xy loglog

xx

dxdy

log

1

xx log1

23log xxyiv

23

1213

xxxx

dxdy

2352

xxx

OR 2log3log xxy

21

31

xxdxdy

23

32

xx

xx

(iii) xy loglog

xx

dxdy

log

1

xx log1

23log xxyiv

23

1213

xxxx

dxdy

2352

xxx

OR 2log3log xxy

21

31

xxdxdy

23

32

xx

xx

2352

xxx

25log

xxyv

252

15122

xxx

xx

dxdy

25log

xxyv

252

15122

xxx

xx

dxdy

25log

xxyv

5

223

2

xx

x

252

15122

xxx

xx

dxdy

25log

xxyv

5

223

2

xx

x

523

xx

252

15122

xxx

xx

dxdy

25log

xxyv

5

223

2

xx

x

523

xx

OR 2log5log xxy

252

15122

xxx

xx

dxdy

25log

xxyv

5

223

2

xx

x

523

xx

OR 2log5log xxy

21

51

xxdxdy

252

15122

xxx

xx

dxdy

25log

xxyv

5

223

2

xx

x

523

xx

OR 2log5log xxy

21

51

xxdxdy

25

52

xxxx

252

15122

xxx

xx

dxdy

25log

xxyv

5

223

2

xx

x

523

xx

OR 2log5log xxy

21

51

xxdxdy

25

52

xxxx

523

xx

252

15122

xxx

xx

dxdy

25log

xxyv

5

223

2

xx

x

xyvi 6log10

523

xx

OR 2log5log xxy

21

51

xxdxdy

25

52

xxxx

523

xx

252

15122

xxx

xx

dxdy

25log

xxyv

5

223

2

xx

x

xyvi 6log10

xdxdy

610log6

523

xx

OR 2log5log xxy

21

51

xxdxdy

25

52

xxxx

523

xx

252

15122

xxx

xx

dxdy

25log

xxyv

5

223

2

xx

x

xyvi 6log10

xdxdy

610log6

10log1

x

523

xx

OR 2log5log xxy

21

51

xxdxdy

25

52

xxxx

523

xx

252

15122

xxx

xx

dxdy

Exercise 12B; 1acf, 2chk, 5acehi, 6b, 7ad, 8acef, 9bd, 10ac, 11, 13a, 14bdfhjl,

15b, 18bdf, 19b, 20af*, 21a*

Exercise 12C; 1bdf, 2, 3, 6, 7a, 8, 11,13, 14, 18*

25log

xxyv

5

223

2

xx

x

xyvi 6log10

xdxdy

610log6

10log1

x

523

xx

OR 2log5log xxy

21

51

xxdxdy

25

52

xxxx

523

xx