Higher Engineering Mathematics, Sixth Edition

Differentiation of hyperbolic functions 333

Now try the following exercise

Exercise 134 Further problemson

differentiation of hyperbolic functions

In Problems 1 to 5 differentiatethe given functions

with respect to the variable:

1. (a) 3sh2x (b) 2ch5θ (c) 4th9t
   [
   (a)6ch2x(b)10sh5θ(c)36sech^2 9t

]

2. (a)

2

3

sech 5x (b)

5

8

cosech

t

2

(c) 2coth7θ

⎡ ⎢ ⎢ ⎢ ⎢ ⎣

(a)−

10

3

sech 5xth5x

(b)−

5

16

cosech

t

2

coth

t

2

(c)−14cosech^27 θ

⎤ ⎥ ⎥ ⎥ ⎥ ⎦

3. (a) 2ln(shx) (b)
   3
   4

ln

(

th

(

θ

2

))

[

(a) 2cothx(b)

3

8

sech

θ

2

cosech

θ

2

]

4. (a) sh2xch2x (b) 3e^2 xth2x
   [
   (a) 2 (sh^22 x+ch^22 x)
   (b)6e^2 x(sech^22 x+th2x)

]

5. (a)

3sh4x

2 x^3

(b)

ch2t

cos2t

⎡

⎢

⎢

⎣

(a)

12 xch4x−9sh4x

2 x^4

(b)

2 (cos 2tsh2t+ch2tsin2t)

cos^22 t

⎤

⎥

⎥

⎦