\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2013c.00648}
\itemau{Ho, Weng Kin; Ho, Foo Him; Lee, Tuo Yeong}
\itemti{Exponential function and its derivative revisited.}
\itemso{Int. J. Math. Educ. Sci. Technol. 44, No. 3, 423-428 (2013).}
\itemab
Summary: Most of the available proofs for $\frac{d}{dx} (e^x)$ 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 $\int_1^X \frac{1}{t} dt$, 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.
\itemrv{~}
\itemcc{I25 I45 I55}
\itemut{exponential function; calculus; teaching of calculus}
\itemli{doi:10.1080/0020739X.2012.703341}
\end