Règles de dérivation :
- \( (x^n)' = n x^{n-1} \)
- \( (a x^n)' = a \cdot n x^{n-1} \)
- \( (u + v)' = u' + v' \)
- Constante → dérivée nulle
Exemple
\(f(x) = 4 \textcolor{blue}{x^3} -5 \textcolor{red}{x^2}+3\textcolor{orange}{x}-9 \)
$f'(x) = 4 \times \textcolor{blue}{3x^2} - 5 \times \textcolor{red}{2x} + 3 \times \textcolor{orange}{1} = 12x^2-10x+3$