Exponential function and its derivative revisited

Abstract

Most of the available proofs for rely on results involving either power series, uniform convergence or a round-about definition of the natural logarithm function ln(x) by the definite integral , and are thus not readily accessible by high school teachers and students. Even instructors of calculus courses avoid showing the complete proof to their undergraduate students because a direct and elementary approach is missing. This short article fills in this gap by supplying a simple proof of the aforementioned basic calculus fact.

Keywords:

• exponential function
• calculus
• teaching of calculus

Notes

Note

1. The results of this survey will be analysed and reported in greater detail in an upcoming report.