Bonjour pouvez vous m'aider stp? Merci

Bonsoir,

Matière : mathématiques
niveau : lycée

Thème abordé : les dérivées

1. f(x) = 3x + 2x² - [tex]{4x^{3}}[/tex]
f ´(x) = 3 + 4x - 12x²

2. f(x) = (x - 2)/(2x + 1)
f(x) = u/v
u = x - 2 => u’ = 1
v = 2x + 1 => v’ = 2
f ‘(x) = (u’v - uv’) / v^2
f ‘(x) = (2x + 1 - 2(x - 2)) / (2x + 1)^2
f ´(x) = (2x + 1 - 2x + 4) / (2x + 1)^2
f ´(x) = 5/(2x + 1)^2

3. f(x) = 4x(-6x - x^4) = -24x^2 - 4x^5
f ´(x) = -48x - 20x^4

4. f(x) = (2x + 3) (4x – 5)
f(x) = u * v
u = 2x + 3 => u’ = 2
v = 4x - 5 => v’ = 4
f ´(x) = u’v + uv’
f ´(x) = 2(4x - 5) + 4(2x + 3)
f ‘(x) = 8x - 10 + 8x + 12
f ´(x) = 16x + 2
f ´(x) = 2(8x + 1)

5. f(x) = 6/(x^2 - 1)
f ´(x) = -12x/(x^2 - 1)^2

6. f(x) = V(2x - 2)
f ´(x) = 2 / [2V(2x - 2)]
f ´(x) = 1/V(2x - 2)

7. f(x) = 3x^2(2x - 1) = 6x^3 - 3x^2
f ´(x) = 18x^2 - 6x
f ´ (x) = 6(3x^2 - x)

8. f(x) = (2 + 3x)(9x² – 1)
f(x) = u * v
u = 2 + 3x => u’ = 3
v = 9x^2 - 1 => v’ = 18x
f ´(x) = u’v + uv’
f ´(x) = 3(9x^2 - 1) + 18x(2 + 3x)
f ‘(x) = 27x^2 - 3 + 36x + 54x
f ´(x) = 27x^2 + 90x - 3
f ´(x) = 3(9x^2 + 30x - 1)

9. f(x) = -2x/(x - 4)
u = -2x => u’ = -2
v = x - 4 => v’ = 1
f ´(x) = [-2(x - 4) - (-2x)] / (x - 4)^2
f ‘(x) = (-2x + 8 + 2x) / (x - 4)^2
f ´(x) = 8/(x - 4)^2

10. f(x) = (2x + 3) – (4x – 5)
f(x) = 2x + 3 - 4x + 5
f(x) = -2x + 8
f ´(x) = -2