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08
3b
(i)
Differentiate loge(cos x) with respect to x.
2

4
(ii)
Hence, or otherwise, evaluate
 tanx
dx.
0
i.
d
[loge(cos x)] =
dx
 s inx
c osx
(as
d
f ' (x)
[logef(x)] =
)
dx
f (x)
= –tan x

4
ii.
 tanx

dx =  loge(c osx)04
0
= – [loge (cos
= – [loge
= – [loge
= – loge
1
2
1
2

- cos 0)]
4
- loge 1]
- 0]
1
2
= loge 2
=
=
1
loge 2 2
1
loge 2
2
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Board of Studies: Notes from the Marking Centre
Source: http://www.boardofstudies.nsw.edu.au/hsc_exams/
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2