OrnaVerum
v 6.30.00
28 Jan 2022
updated 28 Jan 2022

Eqn 13b Help

1) sinh(z) = ½ (ez – e–z) by definition

Substitute z = x/a

The result is sinh(x/a) = ½ (ex/a – e–x/a)
2)
d
dz
cosh(z) = ½
d
dz
(ez + e–z) = ½ (ez – e–z) = sinh(z) by definition
Substitute z = x/a
The result is
d
d(x/a)
cosh(x/a) = sinh(x/a)
ie
d
dx
a cosh(x/a) = sinh(x/a)