Chap. 1
Fonction class="capitalize"
| Fonction | Dérivée | Validité |
|---|---|---|
| ( y = C ) | ( y' = 0 ) | (\mathbb{R}) |
| ( y = x^n ) | ( y' = n x^{n-1} ) | (\mathbb{R}) |
| ( y = \sqrt{x} ) | ( y' = \frac{1}{2 \sqrt{x}} ) | ( x > 0 ) |
| ( y = \frac{1}{x} ) | ( y' = -\frac{1}{x^2} ) | ( x \in \mathbb{R}^* ) |
| ( y = x^\alpha, \alpha \in \mathbb{R} ) | ( y' = \alpha x^{\alpha - 1} ) | ( x > 0 (*) ) |
| ( y = \sin x ) | ( y' = \cos x ) | (\mathbb{R}) |
| ( y = \cos x ) | ( y' = -\sin x ) | (\mathbb{R}) |
| ( y = \tan x ) | ( y' = 1 + \tan^2 x = \frac{1}{\cos^2 x} ) | ( \left] -\frac{\pi}{2}, \frac{\pi}{2} \right[ ) |
| ( y = e^x ) | ( y' = e^x ) | (\mathbb{R}) |
| ( y = \ln x ) | ( y' = \frac{1}{x} ) | ( x > 0 ) |
(*) le domaine de dérivabilité dépend de la valeur de (\alpha).