Exercices de dérivation

Calculer la fonction dérivée des fonctions suivantes

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

version imprimable (derivex.pdf - 38Ko)

Created by Mathematica  (Mars 5, 2006)
Apple, the Apple logo and Macintosh are registered trademarks of Apple Computer, Inc.
All other trademarks and names belong to their rightful owners.Designed, developed and maintained entirely on Mac OS X .