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\begin{document}

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\title{La fonction exponentielle}

\section*{Généralités}

\subsection*{Courbe représentative}

\begin{center}
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\draw[dashed,thick,bleu] (1.5,0) node[below] {$a$} -- (1.5,{exp(1.5)}) -- (0,{exp(1.5)}) node[left] {$\e^a$};
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\subsection*{Propriétés algébriques}
\[
\boxed{
\begin{aligned}
\e^x \times \e^y & = \e^{x+y}\\
\dfrac{1}{\e^x} & = \e^{-x}\\
\dfrac{\e^x}{\e^y} & = \e^{x-y}\\
\big(\e^x\big)^n & = \e^{nx},\ n\in\Z
\end{aligned}
}
\qquad
\boxed{
\begin{aligned}
\e^x = \e^y & \iff  x = y\\
\e^x > \e^y & \iff  x > y\\ 
\e^x < \e^y & \iff  x < y\\
\end{aligned}
}
\]
\section*{Dérivation}
\[
\boxed{\big(\e^x\big)' = \e^x}
\qquad
\boxed{\big(\e^{kx}\big)'=k\e^{kx},\quad k\in\R}
\]
\end{document}