
06164059
j
2013c.00648
Ho, Weng Kin
Ho, Foo Him
Lee, Tuo Yeong
Exponential function and its derivative revisited.
Int. J. Math. Educ. Sci. Technol. 44, No. 3, 423428 (2013).
2013
Taylor \& Francis, Abingdon, Oxfordshire
EN
I25
I45
I55
exponential function
calculus
teaching of calculus
doi:10.1080/0020739X.2012.703341
Summary: Most of the available proofs for $\frac{d}{dx} (e^x)$ rely on results involving either power series, uniform convergence or a roundabout definition of the natural logarithm function $\ln(x)$ by the definite integral $\int_1^X \frac{1}{t} dt$, 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.