12 x1 t05 04 differentiating inverse trig (2013)

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*