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\contentsline {chapter}{AVANT$-$PROPOS}{iii}{chapter*.2}%
\contentsline {chapter}{\numberline {1}Dérivation et ses applications}{1}{chapter.1}%
\contentsline {section}{\numberline {1}Première approche historique}{2}{section.1.1}%
\contentsline {section}{\numberline {2}Nombre dérivé}{3}{section.1.2}%
\contentsline {subsection}{\numberline {1}Approche géométrique}{3}{subsection.1.2.1}%
\contentsline {subsection}{\numberline {2}Définition et exemples fondamentaux}{4}{subsection.1.2.2}%
\contentsline {subsection}{\numberline {3}Interprétations du nombre dérivé}{7}{subsection.1.2.3}%
\contentsline {subsubsection}{\numberline {a}En physique}{7}{subsubsection.1.2.3.1}%
\contentsline {subsubsection}{\numberline {b}En économie}{7}{subsubsection.1.2.3.2}%
\contentsline {section}{\numberline {3}\'Equation de la tangente}{7}{section.1.3}%
\contentsline {subsection}{\numberline {1}Définition}{7}{subsection.1.3.1}%
\contentsline {subsection}{\numberline {2}\'Equation}{8}{subsection.1.3.2}%
\contentsline {section}{\numberline {4}Fonction dérivée}{9}{section.1.4}%
\contentsline {subsection}{\numberline {1}Définition}{9}{subsection.1.4.1}%
\contentsline {subsection}{\numberline {2}Dérivées de référence}{9}{subsection.1.4.2}%
\contentsline {subsection}{\numberline {3}Dérivée d'une fonction composée}{9}{subsection.1.4.3}%
\contentsline {section}{\numberline {5}Fonction valeur absolue}{10}{section.1.5}%
\contentsline {subsection}{\numberline {1}Définition (rappel de Seconde)}{10}{subsection.1.5.1}%
\contentsline {subsection}{\numberline {2}Courbe représentative}{10}{subsection.1.5.2}%
\contentsline {subsection}{\numberline {3}Dérivée}{11}{subsection.1.5.3}%
\contentsline {section}{\numberline {6}Opérations sur les dérivées}{11}{section.1.6}%
\contentsline {section}{\numberline {7}Applications de la dérivation}{13}{section.1.7}%
\contentsline {subsection}{\numberline {1}Variation d'une fonction}{13}{subsection.1.7.1}%
\contentsline {subsection}{\numberline {2}Extremum local}{14}{subsection.1.7.2}%
\contentsline {subsection}{\numberline {3}Méthode de Newton}{14}{subsection.1.7.3}%
\contentsline {subsubsection}{\numberline {a}Formalisation}{16}{subsubsection.1.7.3.1}%
\contentsline {subsubsection}{\numberline {b}Algorithme}{16}{subsubsection.1.7.3.2}%
\contentsline {section}{\color {exotypenumbg}\fontfamily {lmss}\selectfont \large Exercices types}{17}{section*.3}%
\contentsline {section}{\color {exercicenumbg}\fontfamily {lmss}\selectfont \large Exercices}{19}{section*.4}%
\contentsline {subsection}{\fontfamily {lmss}\selectfont Nombre dérivé et tangente}{19}{section*.5}%
\contentsline {subsection}{\fontfamily {lmss}\selectfont Calculs de dérivées}{21}{section*.6}%
\contentsline {subsection}{\fontfamily {lmss}\selectfont Optimisation}{23}{section*.7}%
\contentsline {section}{\color {corrigenumbg}\fontfamily {lmss}\selectfont \large Corrigés des exercices}{27}{section*.8}%
\vspace *{1cm}\hspace *{7mm}\textit {{{\FAtwo \symbol {8}}}~~23 exercices entièrement corrigés}