Mathematical Methods for Physics and Engineering : A Comprehensive Guide

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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.

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