IE 2 : Calcul de dérivées + Correction

(1)

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NOM - Prénom : ...

INTERROGATION ÉCRITE n°2 Classe de TS1-2

Fonction f Dérivée f' Intervalle(s)

f(x) = x⁵ - 4x³ + 2x² + 1 f'(x) =

f(x) = 2x + 1 + 1

x f'(x) =

f(x) = 2x² - 4 3x + 4

f'(x) =

f(x) = (3 - 2x²) x f'(x) =

f(x) = 5x - 3 x

f'(x) =

f(x) = sin(1 - 3x) f'(x) =

f(x) = cos

 

 

x + 1

x f'(x) =

f(x) = 3x² + 2x + 5 f'(x) =

f(x) = (8x² - 5x + 4)³ f'(x) =

f(x) = 1

3x - 5 f'(x) =

f(x) = 1

9x² - 1 f'(x) =

f(x) = 1 - cos x

3 + sin x f'(x) =

f(x) = sin⁵ x f'(x) =

f(x) = 2x

3 - x f'(x) =

f(x) = 1

(x² - 1)⁵ f'(x) =

f(x) = 3 + 2sin² x f'(x) =

(2)

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NOM - Prénom : ...

INTERROGATION ÉCRITE n°2 Classe de TS 1-2

Fonction f Dérivée f' Intervalle(s)

f(x) = x⁵ - 4x³ + 2x² + 1 f'(x) = 5x⁴ - 12x² + 4x IR

f(x) = 2x + 1 + 1

x f'(x) = 2 - 1

x²

]-∞;0[ ou ]0;+∞[

f(x) = 2x² - 4

3x + 4 f'(x) = 6x² + 16x + 12

(3x + 4)²

 

 

-∞ ; - 4

3 ou

 

 

- 43 ; +∞

f(x) = (3 - 2x²) x f'(x) = - 10x² + 3 2 x

]0;+∞[

f(x) = 5x - 3 x

f'(x) = 5x + 3 2x x

]0;+∞[

f(x) = sin(1 - 3x) f'(x) = -3 cos(1 - 3x) IR

f(x) = cos

 

 

x + 1

x f'(x) = -







1 - 1



x² sin

 

 

x + 1

x ]-∞;0[ ou ]0;+∞[

f(x) = 3x² + 2x + 5 f'(x) = 3x + 1 3x² + 2x + 5

IR

f(x) = (8x² - 5x + 4)³ f'(x) = 3(16x - 5)(8x² - 5x + 4)² IR

f(x) = 1

3x - 5 f'(x) = - 3

2(3x - 5) 3x - 5

 

 

53 ; +∞

f(x) = 1

9x² - 1 f'(x) = - 18x

(9x² - 1)²

]

^-^∞^{; -}¹³

[

^ou

]

^{- 1}³^{; 1}³

[

ou

]

¹³^{; +∞}

[

f(x) = 1 - cos x

3 + sin x f'(x) = 1 + 3 sin x - cos x (3 + sin x)²

IR

f(x) = sin⁵ x f'(x) = 5 cos x sin⁴ x IR

f(x) = 2x

3 - x f'(x) = 3 3 - x

(3 - x)² 2x

] 0 ; 3 [

f(x) = 1

(x² - 1)⁵ f'(x) = - 10x

(x² - 1)⁶

] -∞ ; -1 [ ou ] -1 ; 1 [ ou ] 1 ; +∞ [

f(x) = 3 + 2sin² x f'(x) = 2 sin x cos x 3 + 2sin² x

IR