Mathématiques - Chapitre 1 "Fonction D'une Variable" - S1L1
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Course
Mathématiques
Institution
Aix-Marseille (AMU)
Dans ce fichier vous y trouverez tout le contenu du cours de Mathématiques sur le Chapitre 1. Avec toutes les notions, calculs, théorèmes, ou encore des exemples pour approfondir les notions.
OBJECTIFS : Savoir étudier une fonction pour faire de l’économie
- Trouver le sens de variations (↗ ; ↘)
- Les limites pour étudier le comportement à long terme.
- Optimiser (maximiser ou minimiser)
I. RAPPELS SUR LES DÉRIVÉES
1) Calcul des dérivées et applications.
Fonction f Dérivée f’ Intervalle
C (C ∈ R) 0 ℝ
X 1 ℝ
X2 2x ℝ
X3 3x2 ℝ
Xn Nxn-1 ℝ
1 1 ]0, +∞ [ou]-∞, 0[
− !
𝑥 𝑥
√𝑥 1 ]-∞, 0[
2√𝑥
ex ex ]0, +∞[
ln(x) 1 ]0, +∞[
𝑥
- Operations sur les dérivées
U+V U’ + V’ à X2 + ex = 2x + ex
U-V U’ - V’
KU (K∈R) KU’
U*V U’V +V’U
𝑈 𝑈"𝑉 − 𝑉 "𝑈
𝑉 𝑉!
1 −𝑉 "
𝑉 𝑉!
eu U’eu
ln(U) 𝑈"
𝑈
√𝑈 𝑈"
2√𝑈
EXEMPLES :
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