Mathematical Methods for Physics and Engineering : A Comprehensive Guide

3.7 HYPERBOLIC FUNCTIONS

sinh−^1 x

cosech−^1 x

cosech−^1 x

x

2

4

− 2

− 4

− 2 − 1 1 2

Figure 3.15 Graphs of sinh−^1 xand cosech−^1 x.

coth−^1 x

coth−^1 x

tanh−^1 x

x

2

4

− 2

− 4

− 2 − 1 1 2

Figure 3.16 Graphs of tanh−^1 xand coth−^1 x.

hyperbolic functions are given by

d

dx

(coshx)= sinhx, (3.52)

d

dx

(sinhx)=coshx. (3.53)

They may be deduced by considering the definitions (3.38), (3.39) as follows.