Third time lucky.

cosh(x) = [e^x+e^(-x)]/2

sinh(x) = [e^x-e^(-x)]/2

d/dx cosh(x) = sinh(x)

d/dx sinh(x) = cosh(x)

sinh(0) = 0

cosh(0) = 1.

From which the result follows from the definition of a Maclaurin series

(or even more easily by observing from the definition of cosh its power

series representation about 0 contains the even power terms of the

series for the exponential function, and the odd power terms all have

0 for their coefficient, and so don't appear in the expansion)

RonL