Bonjour,
(xⁿ)' = nxⁿ⁻¹
1. f'(x) = 4x - 1
2. f(x) = 2x⁻¹ - 5x ⇒ f'(x) = -2/x² - 5
(exp(x))' = exp(x)
3. f(x) = 3x¹/² + exp(x) ⇒ f'(x) = -(3/2) x⁻¹/² + exp(x) = -3/(2√x) + exp(x)
4. f'(x) = (2x + 2)/5
(u/v)' = (u'v -uv') / v²
d'où (1/v)' = -v'/v²
5. f'(x) = (-2(x - 2) - (1 - 2x)) / (x - 2)² = (-2x + 4 - 1 + 2x) / (x - 2)² = 3 / (x - 2)²
(u.v)' = u'.v + u.v'
6. f'(x) = 2 (5x + 1) + 5 (2x + 3) = 10 x + 2 + 10x + 15 = 20x + 17
7. comme 4
8. comme 2
9. f(x) = 3x . √x + (x³ - 1) /(2√x)
10. f'(x) = -5 / (x - 4)²
11. comme 5
(u o v)' = v' . u' o v
12. f'(x) = -3 exp(-3x + 4)
13. f'(x)(10x - 1) xp(-x) - (5x² - x) exp(-x) = (-5x² + 11x -1) exp(-x)
14. f'(x) = -4 exp(x) / (exp(x) + 1)²
15. f'(x) = -4 exp(x) / (exp(x))² = -4 / exp(x)
16. f'(x) = -2 exp(-2x)
17. f'(x) = ((x² + 3) exp(x) - 2x exp(x)) / (x² + 3)² = (x² - 2x + 3) exp(x) / (x² + 3)²
