Higher Engineering Mathematics, Sixth Edition

Differentiation of inverse trigonometric and hyperbolic functions 335

(a)

(d) (e) (f)

(b) (c)

y

B

A

21 0 11 x

3 /2

23 /2

/2

2 /2

2 



y

y 5 sec^21 x

21 011

3 /2

23 /2

/2

2 /2

2 



x

y

y 5 cosec^21 x

21 0 11

3 /2

23 /2

/2

2 /2



x

y

C

D

21 0 11

23 /2

/2

2 



x

2 /2

3 /2

y

y 5 cot^21 x

0

/2



x

2 /2



y

y 5 tan^21 x

0

/2

x

2 /2

y 5 sin^21 x

y 5 cos^21 x

2 

Figure 33.1

(c)

(c)

y

y 5 tanh^21 x

21 0 11

y

(^3) y 5 sinh (^21) x
2
1
0123
23
22
21
232221 x
(f)
(a)
y
y 5 coth^21 x
210 11
(b)
y
(^3) y 5 cosh (^21) x
2
1
0 123
23
22
21
2221 x
y
(^3) y 5 sech (^21) x
2
1
(^01)
23
22
21
x x
y
(e)
y 5 cosech^21 x
0 x
x
Figure 33.2