1re S1-Mini-Test-Corrigé

Mini-Test – 1

S - Sujet A Correction

a(x) = 6x-7 ; a’(x) = 6 ;

b(x) = 3x²-5x+8 ; b’(x) = 6x-5 ;

c(x) = 7x⁶-3x⁴-2x+1 ; c’(x) = 42x⁵-12x³-2 ; d(x) = (2x-3)(4x+5) ; d’(x) = 16x-2 ; e(x) = (5-x)(5x+7) ; e’(x) = -10x+18 ;

f(x) = (3x²+4x-7)(3x+4) ; f’(x) = 27x²+48x-5 ; g(x) = (5x²+2)(4-2x) ; g’(x) = -30x²+40x-4 ;

n(x) = (5x²+3x-1)² ; n’(x) = 2(10x+3)(5x²+3x-1) ; p(x) = (5x-2)(3x-4)²

p’(x) = 5(3x-4)²+(5x-2)×2×3(3x-4)

= (3x-4)(45x-32)

= 135x²-276x+128 (pas vraiment utile…)

Mini-Test – 1

S - Sujet B Correction

a(x) = 9x-4 ; a’(x) = 9 ;

b(x) = 4x²-3x+7 ; b’(x) = 8x-3 ;

c(x) = 5x⁷-3x⁵-5x+4 ; c’(x) = 35x⁶-15x⁴-5 ; d(x) = (3x-2)(5x+4) ; d’(x) = 30x+2 ; e(x) = (6-x)(3x+9) ; e’(x) = -6x+9 ;

f(x) = (4x²+3x-5)(2x+6) ; f’(x) = 24x²+60x+8 ; g(x) = (6x²+1)(5-3x) ; g’(x) = -54x²+60x-3 ;

n(x) = (4x²+2x+1)² ; n’(x) = 2(8x+2)(4x²+2x+1) ; p(x) = (3x-5)(2x-6)²

p’(x) = 3(2x-6)²+(3x-5)×2×2(2x-6) = (2x-6)(18x-38)

= 36x²-184x+228 (pas vraiment utile…)