Exercices-Calcul-derivees

Fonction d´eriv´ee: du calcul !!
Calculer les fonctions d´eriv´ees f′(x) dans tous les cas suivants.
´
Ecrire la fonction d´eriv´ee sous la forme la plus ”simplifi´ee” possible : une seule fraction au plus (mˆeme
d´enominateur . . .), et le plus factoris´e possible.
f1(x) = x3 −5x7+3
xf2(x) = 1 2x4
−x√3 + 3√x f3(x) = (x2+ 3) x5f4(x) = (3x−2)2
f5(x) = x2√x f6(x) = (x+ 3)x2√x f7(x) = x+1
xx f8(x) = x+2 x2x
f9(x) = 3
x+ 1 f10(x) = −25 x2+ 3 f11(x) = 5x x2+ 3 f12(x) = x+ 2 x+ 3
f13(x) = x2+ 1
x3+ 1 f14(x) = √x x2+ 3 f15(x) =
x−
1
x
x+1
x
f16(x) =
x2+3
x
x2+x
3
f17(x) = 5√x
1 + 2
x
f18(x) = x
1 + 1
x
3 + 3
x
f19(x) =1+ 1
√x 1−
1
√xf20(x) = 1
3x
3 + 9
x
x2+ 2
f′
1(x) = 3x4
−35x8 −3
x2f′
2(x) = 4x3√x−2√3x+ 3
2√xf′
3(x) = x4(7x2+ 15) f′ 4(x) = 6(3x−2)
f′
5(x) = 5
2x√x f′
6(x) = 1
2x√x(7x+ 15) f′
7(x) = 2x f ′ 8(x) = 2 (x3
−1)
x2
f′
9(x) = −3
(x+ 1)2f′
10(x) = 20x
(x2+ 3)2f′
11(x) = 5 −x2+ 3
(x2+ 3)2f′
12(x) = 1
(x+ 3)2
f′
13(x) = −x(x3+ 3x−2)
(x3+ 1)2f′
14(x) =−3(x−1)(x+ 1)
2√x(x2+ 3)2f′
15(x) = 4x
(x2+ 1)2f′
16(x) = 3x3
−27x−6
x(3x2+x)2
f′
17(x) = 5√x(x+ 6)
2 (x+ 2)2f′
18(x) = 1
3f′
19(x) = 1
x2f′
20(x) = −x2
−6x+ 2
(x2+ 2)2
Y. Morel - xymaths.free.fr Fonction d´eriv´ee: du calcul !! - 1`ere S - 1/1