12x1 t01 02 differentiating logs (2010)
TRANSCRIPT
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