Differentiation of hyperbolic functions 333
Now try the following exercise
Exercise 134 Further problems on
differentiation of hyperbolic functions
In Problems 1 to 5 differentiate the given functions
with respect to the variable:
1. (a) 3 sh 2x (b) 2 ch 5θ (c) 4 th9t
(a) 6 ch2x (b) 10 sh 5θ (c) 36 sech 2 9t
2. (a)
2
3
sech 5x (b)
5
8
cosech
t
2
(c) 2 coth 7θ
⎡
⎢
⎢
⎢
⎢
⎣
(a) −
10
3
sech 5x th 5x
(b) −
5
16
cosech
t
2
coth
t
2
(c) −14 cosech 2 7θ
⎤
⎥
⎥
⎥
⎥
⎦
3. (a) 2 ln (sh x) (b)
3
4
ln
th
θ
2
(a) 2 coth x (b)
3
8
sech
θ
2
cosech
θ
2
4. (a) sh 2x ch 2x (b) 3e 2x th 2x
(a) 2(sh 2 2x + ch 2 2x)
(b) 6e 2x (sech
2 2x + th 2x)
5. (a)
3 sh4x
2x 3
(b)
ch 2t
cos 2t
⎡
⎢
⎢
⎣
(a)
12x ch 4x − 9 sh4x
2x 4
(b)
2(cos 2t sh 2t + ch 2t sin 2t )
cos 2 2t
⎤
⎥
⎥
⎦