Download - 12X1 T03 03 differentiating trig functions
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Differentiating Trig
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Differentiating Trig0sinlim
0
x
x
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Differentiating Trig0sinlim
0
x
x
1coslim0
xx
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Differentiating Trig0sinlim
0
x
x
1coslim0
xx
0tanlim0
xx
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Differentiating Trig0sinlim
0
x
x Sector Area OAC
1coslim0
xx
0tanlim0
xx
O A
C
1x
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Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea
1coslim0
xx
0tanlim0
xx
O A
C
1x
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Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea AOB Area
1coslim0
xx
0tanlim0
xx
O A
C
1x
B
tan
x
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Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea AOB Area
xxx tan1211
21sin11
21 2 1coslim
0
x
x
0tanlim0
xx
O A
C
1x
B
tan
x
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Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea AOB Area
xxx tan1211
21sin11
21 2 1coslim
0
x
x
0tanlim0
xx
O A
C
1x
B
tan
x
xxx tansin
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Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea AOB Area
xxx tan1211
21sin11
21 2 1coslim
0
x
x
0tanlim0
xx
O A
C
1x
B
tan
x
xxx tansin
xx
xx
xx
sintan
sinsinsin
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Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea AOB Area
xxx tan1211
21sin11
21 2 1coslim
0
x
x
0tanlim0
xx
O A
C
1x
B
tan
x
xxx tansin
xx
xx
xx
sintan
sinsinsin
xxx
cos1
sin1
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Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea AOB Area
xxx tan1211
21sin11
21 2 1coslim
0
x
x
0tanlim0
xx
O A
C
1x
B
tan
x
xxx tansin
xx
xx
xx
sintan
sinsinsin
xxx
cos1
sin1
1sin
1
0as
xx
x
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Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea AOB Area
xxx tan1211
21sin11
21 2
1sin
lim0
x
xx
1coslim0
xx
0tanlim0
xx
O A
C
1x
B
tan
x
xxx tansin
xx
xx
xx
sintan
sinsinsin
xxx
cos1
sin1
1sin
1
0as
xx
x
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e.g. x
xix 5sin
5lim0
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e.g. x
xix 5sin
5lim0
1
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0 xx
x 3sin3
31lim
0
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0 xx
x 3sin3
31lim
0
31
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
xy sinx
xx 3sin
331lim
0
31
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
xy sin
h
xhxdxdy
x
sinsinlim0
xx
x 3sin3
31lim
0
31
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
xy sin
h
xhxdxdy
x
sinsinlim0
xx
x 3sin3
31lim
0
31
hxxx
x
sinsinhcoscoshsinlim0
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
xy sin
h
xhxdxdy
x
sinsinlim0
xx
x 3sin3
31lim
0
31
hxxx
x
sinsinhcoscoshsinlim0
hx
hx
x
1coshsinsinhcoslim0
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
xy sin
h
xhxdxdy
x
sinsinlim0
xx
x 3sin3
31lim
0
31
hxxx
x
sinsinhcoscoshsinlim0
hx
hx
x
1coshsinsinhcoslim0
h
h
xh
xx
22
cos2sinsinhcoslim
2
0
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
xy sin
h
xhxdxdy
x
sinsinlim0
xx
x 3sin3
31lim
0
31
hxxx
x
sinsinhcoscoshsinlim0
hx
hx
x
1coshsinsinhcoslim0
h
h
xh
xx
22
cos2sinsinhcoslim
2
0 1cos22cos 2
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e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
xy sin
h
xhxdxdy
x
sinsinlim0
xx
x 3sin3
31lim
0
31
hxxx
x
sinsinhcoscoshsinlim0
hx
hx
x
1coshsinsinhcoslim0
h
h
xh
xx
22
cos2sinsinhcoslim
2
0 1cos22cos 2
h
h
xh
xx
2sin2
sinsinhcoslim2
0
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
xfy sin
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx xfy sin
xfxfdxdy cos
xcos
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
xfy sin
xfxfdxdy cos
xy cos
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
xfy sin
xfxfdxdy cos
xy cos
xy
2sin
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
xfy sin
xfxfdxdy cos
xy cos
xy
2sin
x
dxdy
2cos
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
xfy sin
xfxfdxdy cos
xy cos
xy
2sin
x
dxdy
2cos
xsin
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
xfy sin
xfxfdxdy cos
xy cos
xy
2sin
x
dxdy
2cos
xsin
xfy cos
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2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
xfy sin
xfxfdxdy cos
xy cos
xy
2sin
x
dxdy
2cos
xsin
xfy cos
xfxfdxdy sin
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xy tan
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xy tan
xxy
cossin
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
x
yii 1tan
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
x
yii 1tan
xxdxdy 1sec1 2
2
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
x
yii 1tan
xxdxdy 1sec1 2
2
xyiii coslog
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
x
yii 1tan
xxdxdy 1sec1 2
2
xyiii coslog
xx
dxdy
cossin
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
x
yii 1tan
xxdxdy 1sec1 2
2
xyiii coslog
xx
dxdy
cossin
xtan
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
x
yii 1tan
xxdxdy 1sec1 2
2
xyiii coslog
xx
dxdy
cossin
xtan
xyiv 5tan
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
x
yii 1tan
xxdxdy 1sec1 2
2
xyiii coslog
xx
dxdy
cossin
xtan
xyiv 5tan
xxdxdy 24 sectan5
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
x
yii 1tan
xxdxdy 1sec1 2
2
xyiii coslog
xx
dxdy
cossin
xtan
xyiv 5tan
xxdxdy 24 sectan5
xeyv cos
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xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
3sin e.g. xyi 32 cos3 xx
dxdy
x
yii 1tan
xxdxdy 1sec1 2
2
xyiii coslog
xx
dxdy
cossin
xtan
xyiv 5tan
xxdxdy 24 sectan5
xeyv cos xx ee
dxdy sin
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Exercise 14F; 2, 4, 5
Exercise 14G; 2ace etc, 3ace etc, 5ace etc, 6, 7ab(i), 8, 12, 13c, 16a*
Exercise 14H; 2 ac, 4bd, 6, 8, 14, 17, 20