We apply the arguments from elementary calculus that are used to differentiate cosine and sine to hyperbolic cosine and hyperbolic sine, and by so doing produce the natural exponential function by ...

Stephen R. Wassell, Superexponentiation and Fixed Points of Exponential and Logarithmic Functions, Mathematics Magazine, Vol. 73, No. 2 (Apr., 2000), pp. 111-119 ...

First we have proportional parts of all numbers up to 100; then on one page three-place logarithms of numbers and of the six trigonometric functions, natural and logarithmic.

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...