12X1 T05 04 differentiating inverse trig (2010)
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Transcript of 12X1 T05 04 differentiating inverse trig (2010)
Differentiating Inverse Trig
Differentiating Inverse Trigxy 1sin
Differentiating Inverse Trigxy 1sin
yx sin
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cos
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cosyx cos
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cosyx cos
ydydx sin
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cosyx cos
ydydx sin
ydxdy
sin1
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cosyx cos
ydydx sin
ydxdy
sin1
2
2
2
11cos11
sin1
x
y
y
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cosyx cos
ydydx sin
ydxdy
sin1
2
2
2
11cos11
sin1
x
y
y
xy 1tan
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cosyx cos
ydydx sin
ydxdy
sin1
2
2
2
11cos11
sin1
x
y
y
xy 1tanyx tan
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cosyx cos
ydydx sin
ydxdy
sin1
2
2
2
11cos11
sin1
x
y
y
xy 1tanyx tan
ydydx 2sec
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cosyx cos
ydydx sin
ydxdy
sin1
2
2
2
11cos11
sin1
x
y
y
xy 1tanyx tan
ydydx 2sec
ydxdy
2sec1
Differentiating Inverse Trigxy 1sin
yx sin
ydydx cos
ydxdy
cos1
2
2
2
11
sin11
cos1
x
y
y
xy 1cosyx cos
ydydx sin
ydxdy
sin1
2
2
2
11cos11
sin1
x
y
y
xy 1tanyx tan
ydydx 2sec
ydxdy
2sec1
2
2
11tan11
x
y
In general;
axy 1sin
In general;
axy 1sin
22
1xadx
dy
In general;
axy 1sin
22
1xadx
dy
axy 1cos
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
21 xfxf
dxdy
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
21 xfxf
dxdy
xfy 1cos
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
21 xfxf
dxdy
xfy 1cos
21 xfxf
dxdy
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
21 xfxf
dxdy
xfy 1cos
21 xfxf
dxdy
xfy 1tan
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
21 xfxf
dxdy
xfy 1cos
21 xfxf
dxdy
xfy 1tan
21 xfxf
dxdy
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
21 xfxf
dxdy
xfy 1cos
21 xfxf
dxdy
xfy 1tan
21 xfxf
dxdy
e.g. xyi 5sin 1
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
21 xfxf
dxdy
xfy 1cos
21 xfxf
dxdy
xfy 1tan
21 xfxf
dxdy
e.g. xyi 5sin 1
22515
xdxdy
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
21 xfxf
dxdy
xfy 1cos
21 xfxf
dxdy
xfy 1tan
21 xfxf
dxdy
e.g. xyi 5sin 1
22515
xdxdy
xeyii 1cos
In general;
axy 1sin
22
1xadx
dy
axy 1cos
22
1xadx
dy
axy 1tan
22 xaa
dxdy
xfy 1sin
21 xfxf
dxdy
xfy 1cos
21 xfxf
dxdy
xfy 1tan
21 xfxf
dxdy
e.g. xyi 5sin 1
22515
xdxdy
xeyii 1cos
x
x
ee
dxdy
21
3sin 1 xyiii
3sin 1 xyiii
291
xdxdy
3sin 1 xyiii
291
xdxdy
OR
3sin 1 xy
3sin 1 xyiii
291
xdxdy
OR
3sin 1 xy
91
31
2xdxdy
3sin 1 xyiii
291
xdxdy
OR
3sin 1 xy
91
31
2xdxdy
2
2
91
931
31
x
x
3sin 1 xyiii
291
xdxdy
OR
3sin 1 xy
91
31
2xdxdy
2
2
91
931
31
x
x
xeyiv1cos
3sin 1 xyiii
291
xdxdy
OR
3sin 1 xy
91
31
2xdxdy
2
2
91
931
31
x
x
xeyiv1cos
xexdx
dy 1cos21
1
3sin 1 xyiii
291
xdxdy
OR
3sin 1 xy
91
31
2xdxdy
2
2
91
931
31
x
x
xeyiv1cos
xexdx
dy 1cos21
1
2
cos
1
1
xe x
31tan xyv
31tan xyv
2
21
11tan3x
xdxdy
31tan xyv
2
21
11tan3x
xdxdy
2
21
1tan3
xx
31tan xyv
2
21
11tan3x
xdxdy
2
21
1tan3
xx
312 tan xxyvi
31tan xyv
2
21
11tan3x
xdxdy
2
21
1tan3
xx
312 tan xxyvi
xxx
xxdxdy 2tan
13 31
6
22
31tan xyv
2
21
11tan3x
xdxdy
2
21
1tan3
xx
312 tan xxyvi
xxx
xxdxdy 2tan
13 31
6
22
316
4
tan213 xx
xx
31tan xyv
2
21
11tan3x
xdxdy
2
21
1tan3
xx
312 tan xxyvi
xxx
xxdxdy 2tan
13 31
6
22
316
4
tan213 xx
xx
Exercise 1D; 2ace etc, 3bd,4a, 5, 6a, 9ace etc, 11, 13,
14, 20a*