Réponse :
Explications étape par étape
Bonjour
Dérivées :
Elles sont toutes du type :
f ´(x) = (u’v - uv’)/v^2
f(x) = 2x/(5x - 4)
u = 2x => u’ = 2
v = 5x - 4 => v’ = 5
f ‘(x) = (2 * (5x - 4) - 5(2x))/(5x - 4)^2
f ´(x) = (10x - 8 - 10x)/(5x - 4)^2
f ´(x) = -8/(5x - 4)^2
f(x) = e^x / (3x + 6)
u = e^x => u’ = e^x
v = 3x + 6 => v’ = 3
f ‘(x) = [e^x(3x + 6) - e^x * 3]/(3x + 6)^2
f ´(x) = (3xe^x + 6e^x - 3e^x)/(3x + 6)^2
f ´(x) = (3xe^x + 3e^x)/(3x + 6)^2
f(x) = (4x - 2)/e^x
u = 4x - 2 => u’ = 4
v = e^x => v’ = e^x
f ‘(x) = [4e^x - (4x - 2) * e^x]/(e^x)^2
f ‘(x) = (4e^x - 4xe^x + 2e^x)/e^(2x)
f ´(x) = (6e^x - 4xe^x)/e^(2x)
f ´(x) = e^x(6 - 4x)/e^(2x)
f ´(x) = (6 - 4x)/e^x
f(x) = (5x^2 - 2x + 3) / (6x - 2)
u = 5x^2 - 2x + 3 => u’ = 5 * 2x^(2-1) - 2 = 10x - 2
v = 6x - 2 => v’ = 6
f ´(x) = [(10x - 2) * (6x - 2) - 6(5x^2 - 2x + 3)]/(6x - 2)^2
f ‘(x) = (60x^2 - 20x - 12x + 4 - 30x^2 + 12x - 18)/(6x - 2)^2
f ´(x) = (30x^2 - 20x - 14)/(6x - 2)^2
