Differentiating Trig
Differentiating Trig0sinlim
0
x
x
Differentiating Trig0sinlim
0
x
x
1coslim0
xx
Differentiating Trig0sinlim
0
x
x
1coslim0
xx
0tanlim0
xx
Differentiating Trig0sinlim
0
x
x Sector Area OAC
1coslim0
xx
0tanlim0
xx
O A
C
1x
Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea
1coslim0
xx
0tanlim0
xx
O A
C
1x
Differentiating Trig0sinlim
0
x
x Sector Area OACAOCArea AOB Area
1coslim0
xx
0tanlim0
xx
O A
C
1x
B
tan
x
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
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
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
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
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
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
e.g. x
xix 5sin
5lim0
e.g. x
xix 5sin
5lim0
1
e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0 xx
x 3sin3
31lim
0
e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0 xx
x 3sin3
31lim
0
31
e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
xy sinx
xx 3sin
331lim
0
31
e.g. x
xix 5sin
5lim0
1 x
xiix 3sinlim
0
xy sin
h
xhxdxdy
x
sinsinlim0
xx
x 3sin3
31lim
0
31
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
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
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
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
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
2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx
xcos
xfy sin
2
2sin
sinsinhcoslim2
0 h
h
xh
xx
2sin
2
2sin
sinsinhcoslim0
hh
h
xh
xx
0sin1cos xx xfy sin
xfxfdxdy cos
xcos
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
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
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
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
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
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
xy tan
xy tan
xxy
cossin
xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xy tan
xxy
cossin
xxx
xxxxx
dxdy
2
22
2
cossincos
cossinsincoscos
xx
2
2
seccos
1
xfy tan
xfxfdxdy 2sec
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
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
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
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
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
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
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
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
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
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
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
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
Recommended