Bonjour,
1)
f(x) = (-x² + 3x + 2)(x + 3)
u(x) = -x² + 3x + 2
u'(x) = -2x + 3
v(x) = x + 3
v'(x) = 1
f'(x) = (-2x + 3) × (x + 3) + (-x² + 3x + 2) × 1
= -2x² - 6x + 3x + 9 -x² + 3x + 2
= -3x² + 11
2)
f(x) = (x³ - 2x + 19)(- x² + 5x)
u(x) = x³ - 2x + 19
u'(x) = 3x² - 2
v(x) = - x² +5x
v'(x) = -2x + 5
f'(x) = (3x² - 2) × (- x² +5x) + (x³ - 2x + 19) + (-2x + 5)
= -3x⁴ - 15x³ + 2x² - 10x - 2x⁴ + 5x³ + 4x² - 10x - 38x + 95
= - 5x⁴ + 20x³ + 6x² - 58x + 95
3)
f(x) = 3x sin x
u(x) = 3x
u'(x) = 3
v(x) = sin x
v'(x) = cos x
f'(x) = 3sin x + 3xcos x
4)
f(x) = (4x + 2)(-3x + 4)
u(x) = 4x + 2
u'(x) = 4
v(x) = -3x + 4
v'(x) = - 3
f'(x) = 4 × (-3x + 4) + (4x + 2) × (-3)
= -12x + 16 - 12x - 6
= -24x + 10
5)
f(x) = x⁹ - 3x⁷ + 29x² + 2022
f'(x) = 9x⁸ - 21x⁶ + 58x
