Calculer la fonction dérivée des fonctions suivantes - Solutions - Format pdf

f(x) =  -5 x

f(x) = 3 x

f(x) = x + 2

f(x) = 5 - 7 x

f(x) = 2 x^2 - 5 x + 6

f(x) = 3 x^5 - 2 x^3 + 3 x^2 - 7 x + 2

f(x) = 2 x^(1/2)

f(x) = x^(1/2) - 3 x^2

f(x) = x^(1/3) + 2

f(x) = 5 x - 1/x

f(x) = 5/x^(1/3)

f(x) = 2/x^2 - 3/x^3

f(x) =  (x + 1) (3 x - 2)

f(x) =  (x + 5) (2 x - 3)

f(x) = x^(1/2) (x^2 - 1)

f(x) =  (x + 2)/(x - 3)

f(x) =  (2 x^2 - 1)/(x + 5)

f(x) =  (x - 2)^3

f(x) =  (5 x - 4)^6

Solutions

f'(x) =  (-5 x)^′ =  -5

f'(x) =  (3 x)^′ = 3

f'(x) =  (x + 2)^′ = 1

f'(x) =  (5 - 7 x)^′ =  -7

f'(x) =  (2 x^2 - 5 x + 6)^′ = 4 x - 5

f'(x) =  (3 x^5 - 2 x^3 + 3 x^2 - 7 x + 2)^′ = 15 x^4 - 6 x^2 + 6 x - 7

f'(x) =  (2 x^(1/2))^′ = 1/x^(1/2)

f'(x) =  (x^(1/2) - 3 x^2)^′ = 1/(2 x^(1/2)) - 6 x

f'(x) =  (x^(1/3) + 2)^′ = 1/(3 x^(2/3))

f'(x) =  (5 x - 1/x)^′ = 5 + 1/x^2

f'(x) = 5/x^(1/3)^′ =  -5/(3 x^(4/3))

f'(x) =  (2/x^2 - 3/x^3)^′ = 9/x^4 - 4/x^3 =  (9 - 4 x)/x^4

f'(x) =  ((x + 1) (3 x - 2))^′ = 3 x + 3 (x + 1) - 2 = 6 x + 1

f'(x) =  ((x + 5) (2 x - 3))^′ = 2 x + 2 (x + 5) - 3 = 4 x + 7

f'(x) =  (x^(1/2) (x^2 - 1))^′ = 2 x^(3/2) + (x^2 - 1)/(2 x^(1/2))  =  (5 x^2 - 1)/(2 x^(1/2))

f'(x) =  (x + 2)/(x - 3)^′ = 1/(x - 3) - (x + 2)/(x - 3)^2 =  -5/(x - 3)^2

f'(x) =  (2 x^2 - 1)/(x + 5)^′ =  (4 x)/(x + 5) - (2 x^2 - 1)/(x + 5)^2 =  (2 x^2 + 20 x + 1)/(x + 5)^2

f'(x) =  (x - 2)^3^′ = 3 (x - 2)^2

f'(x) =  (5 x - 4)^6^′ = 30 (5 x - 4)^5

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