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:
- (a) 3sh2x (b) 2ch5θ (c) 4th9t
[
(a)6ch2x(b)10sh5θ(c)36sech^2 9t
]
- (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
⎤ ⎥ ⎥ ⎥ ⎥ ⎦
- (a) 2ln(shx) (b)
3
4
ln
(
th
(
θ
2
))
[
(a) 2cothx(b)
3
8
sech
θ
2
cosech
θ
2
]
- (a) sh2xch2x (b) 3e^2 xth2x
[
(a) 2 (sh^22 x+ch^22 x)
(b)6e^2 x(sech^22 x+th2x)
]
- (a)
3sh4x
2 x^3
(b)
ch2t
cos2t
⎡
⎢
⎢
⎣
(a)
12 xch4x−9sh4x
2 x^4
(b)
2 (cos 2tsh2t+ch2tsin2t)
cos^22 t
⎤
⎥
⎥
⎦