QCM AUTO - EVALUATION
2 – ANALYSE 2.3 – DERIVATION 2.3.3 EXPRESSIONS DE DERIVEES
QCM 2.3.3.1 : dérivées
1) f x
( ) (
=x x+1)
; f′( )
x =...1 2 2x 2x+1
2)
( )
;( )
...1 ′
= =
+
f x x f x
x
( )
21 +1
x
(
+1)
2x
x
( )
21 1
− +
x
(
−+1)
2x x
3) f x
( )
=ln(
x2+1)
; f′( )
x =...2
1 +1
x 2
2 +1 x
x ln
(
x12+1)
ln(
x22x+1)
4) f x
( )
=sin(
ω ϕt+)
; f′( )
x =...( )
cos ω ϕt+ −cos
(
ω ϕt+)
ωcos(
ω ϕt+)
−ωcos(
ω ϕt+)
5) f x
( )
= sin( )
2x ; f′( )
x =...( ) ( )
cos sin
2
2 2
x x
( ) ( )
cos sin
2 2
2 x x
( ) ( )
cos sin
2 2
x x
( ) ( )
cos sin
2 2
2
× x
x
6) f x
( )
=e1x ; f′( )
x =...1 1
ex x
1
ex ln
1
×ex x
1 2
1e
− x x
7) f x
( )
=(
x2+1)
3 ; f′( )
x =...(
2)
26x x +1 2x x
(
2+1)
3 2x x(
2+1)
2 3(
x2+1)
28) f x
( ) ( )
= lnx 2 ; f′( )
x =...2 x
1 x
2ln x x
1ln x x
9) f x
( )
=ln( )
2x ; f′( )
x =...2 x
1 x
1 2x
1 4x 10) La dérivée de f x
( )
3 est( )
2 2
3x f′ 3x 3f′
