3x² Df = Df

Première S2 Exercices sur le chapitre 8 : E3 et E4. 2007 2008

E3 Savoir utiliser les premières formules sur les dérivées.

Calculons f ' ( x ) et précisons l'ensemble de définition de f et de f '.

1 ) f ( x ) = x² f ' ( x ) = 2x D_f = D_f' = .

2 ) f ( x ) = x³ f ' ( x ) = 3x² D_f = D_f' = .

3 ) f ( x ) = x⁴ f ' ( x ) = 4x³ D_f = D_f' = .

4 ) f ( x ) = 5 f ' ( x ) = 0 D_f = D_f' = .

5 ) f ( x ) = -6 f ' ( x ) = 0 D_f = D_f' = .

6 ) f ( x ) = 1

x f ' ( x ) = -

² x

1 _D

f = D_f' = ^*.

7 ) f ( x ) =

² x

1 _{= x}^-2 f ' ( x ) = - 2 x^-3 = - x3

2 D_f = D_f' = ^*.

8 ) f ( x ) = ₃

x1 = x^-3 f ' ( x ) = - 3 x^-4 = - ₄ x

3 D_f = D_f' = ^*.

9 ) f ( x ) =

x1 = x4 ^-4 f ' ( x ) = - 4 x^-5 = - x5

4 D_f = D_f' = ^*.

E4 Savoir dériver une somme.

Calculons f ' ( x ) et précisons l'ensemble de définition de f et de f '.

1 ) f ( x ) = x² + x³ f ' ( x ) = 2x + 3x² D_f = D_f' = .

2 ) f ( x ) = x⁴ + 5 f ' ( x ) = 4x³ D_f = D_f' = .

3 ) f ( x ) = -6 + 1

x f ' ( x ) = -

²

x1 D_f = D_f' = ^*.

4 ) f ( x ) =

² x1 + ₃

x

1 f ' ( x ) = - ₃

x2 - ₄ x

3 D_f = D_f' = ^*.

5 ) f ( x ) = ₄

x1 + x f ' ( x ) = - ₅

x4 + x 2

1 _D

f = D_f' = ] 0 ; + ∞ [.

6 ) f ( x ) = 1 + x² + x³ + ₄ x

1 f ' ( x ) = 2x + 3x² - ₅ x

4 _D

f = D_f' = ^*.