98 lines
2.9 KiB
TeX
98 lines
2.9 KiB
TeX
|
\documentclass[a4paper,10pt, table]{/media/documents/Cours/Prof/Enseignements/2014-2015/Archive/2014-2015/tools/style/classCours}
|
||
|
|
\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/Archive/2014-2015/2014_2015}
|
||
|
|
|
||
|
|
% Title Page
|
||
|
|
\titre{Opération sur les fonctions}
|
||
|
|
% \seconde \premiereS \PSTMG \TSTMG
|
||
|
|
\classe{\premiereS}
|
||
|
|
\date{Mai 2015}
|
||
|
|
|
||
|
|
\begin{document}
|
||
|
|
|
||
|
|
\thispagestyle{empty}
|
||
|
|
|
||
|
|
\begin{center}
|
||
|
|
\begin{tabular}{|p{5cm}|p{5cm}|}
|
||
|
|
\hline
|
||
|
|
Fonction & Dérivée \\
|
||
|
|
\hline
|
||
|
|
$f(x) = u(x) + v(x)$ & $f'(x) = u'(x) + v'(x)$ \\
|
||
|
|
\hline
|
||
|
|
$f(x) = u(x) \times v(x)$ & $f'(x) = u'(x)v(x) + u(x)v'(x)$ \\
|
||
|
|
\hline
|
||
|
|
$f(x) = \dfrac{1}{u(x)}$ & $f'(x) = \dfrac{-u'(x)}{u(x)^2}$\\
|
||
|
|
\hline
|
||
|
|
$f(x) = \dfrac{u(x)}{v(x)}$ & $f'(x) = \dfrac{u'(x)v(x) - u(x)v'(x)}{v(x)^2}$ \\
|
||
|
|
\hline
|
||
|
|
\end{tabular}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
\begin{Ex}
|
||
|
|
\begin{enumerate}
|
||
|
|
\item Dériver puis étudier les variations de $f(x) = \sqrt{x}(2x+1)$
|
||
|
|
\item Dériver puis étudier les variations de $g(x) = \dfrac{1}{2x^2 + 4x - 1}$
|
||
|
|
\item Dériver puis étudier les variations de $h(x) = \dfrac{3x^2 - x - 1}{4x - 1}$
|
||
|
|
\end{enumerate}
|
||
|
|
\end{Ex}
|
||
|
|
|
||
|
|
\vfill
|
||
|
|
|
||
|
|
\begin{center}
|
||
|
|
\begin{tabular}{|p{5cm}|p{5cm}|}
|
||
|
|
\hline
|
||
|
|
Fonction & Dérivée \\
|
||
|
|
\hline
|
||
|
|
$f(x) = u(x) + v(x)$ & $f'(x) = u'(x) + v'(x)$ \\
|
||
|
|
\hline
|
||
|
|
$f(x) = u(x) \times v(x)$ & $f'(x) = u'(x)v(x) + u(x)v'(x)$ \\
|
||
|
|
\hline
|
||
|
|
$f(x) = \dfrac{1}{u(x)}$ & $f'(x) = \dfrac{-u'(x)}{u(x)^2}$\\
|
||
|
|
\hline
|
||
|
|
$f(x) = \dfrac{u(x)}{v(x)}$ & $f'(x) = \dfrac{u'(x)v(x) - u(x)v'(x)}{v(x)^2}$ \\
|
||
|
|
\hline
|
||
|
|
\end{tabular}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
\begin{Ex}
|
||
|
|
\begin{enumerate}
|
||
|
|
\item Dériver puis étudier les variations de $f(x) = \sqrt{x}(2x+1)$
|
||
|
|
\item Dériver puis étudier les variations de $g(x) = \dfrac{1}{2x^2 + 4x - 1}$
|
||
|
|
\item Dériver puis étudier les variations de $h(x) = \dfrac{3x^2 - x - 1}{4x - 1}$
|
||
|
|
\end{enumerate}
|
||
|
|
\end{Ex}
|
||
|
|
|
||
|
|
\vfill
|
||
|
|
|
||
|
|
\begin{center}
|
||
|
|
\begin{tabular}{|p{5cm}|p{5cm}|}
|
||
|
|
\hline
|
||
|
|
Fonction & Dérivée \\
|
||
|
|
\hline
|
||
|
|
$f(x) = u(x) + v(x)$ & $f'(x) = u'(x) + v'(x)$ \\
|
||
|
|
\hline
|
||
|
|
$f(x) = u(x) \times v(x)$ & $f'(x) = u'(x)v(x) + u(x)v'(x)$ \\
|
||
|
|
\hline
|
||
|
|
$f(x) = \dfrac{1}{u(x)}$ & $f'(x) = \dfrac{-u'(x)}{u(x)^2}$\\
|
||
|
|
\hline
|
||
|
|
$f(x) = \dfrac{u(x)}{v(x)}$ & $f'(x) = \dfrac{u'(x)v(x) - u(x)v'(x)}{v(x)^2}$ \\
|
||
|
|
\hline
|
||
|
|
\end{tabular}
|
||
|
|
\end{center}
|
||
|
|
|
||
|
|
\begin{Ex}
|
||
|
|
\begin{enumerate}
|
||
|
|
\item Dériver puis étudier les variations de $f(x) = \sqrt{x}(2x+1)$
|
||
|
|
\item Dériver puis étudier les variations de $g(x) = \dfrac{1}{2x^2 + 4x - 1}$
|
||
|
|
\item Dériver puis étudier les variations de $h(x) = \dfrac{3x^2 - x - 1}{4x - 1}$
|
||
|
|
\end{enumerate}
|
||
|
|
\end{Ex}
|
||
|
|
|
||
|
|
|
||
|
|
\end{document}
|
||
|
|
|
||
|
|
%%% Local Variables:
|
||
|
|
%%% mode: latex
|
||
|
|
%%% TeX-master: "master"
|
||
|
|
%%% End:
|
||
|
|
|