Functie Afgeleide f `(x)= Primitieve F(x)= / = 4 / = 34 f (x)= (x!4)3 f (x

Functie Primitieve F(x) = Afgeleide f ' (x) = ! ! = ! ! !
! ! = 3! f (x) = (x ! 4) 3
f (x) = 3(2 ! x)4 f ' (x) = !12(2 ! x)3 1
1
3
F(x) = 3• (2 ! x)5 • + c = ! (2 ! x)5 + c 5
!1
5
1
1
1
5
F(x) = (2x ! 3)5 • + c = ( 2x ! 3) + c 5
2
10
! ! = (2! − 3)! ! ! = (3 − 2!)! f (x) = 4(3! 2x) •!2 = !8(3! 2x) '
3
3
! ! = 5(2! − 3)! f (x) = e 1
1
1
5
F(x) = (3! 2x)5 • + c = ! (3! 2x ) + c 5
!2
10
1
1
1
5
F(x) = 5• (2x ! 3)5 • + c = ( 2x ! 3) + c 5
2
2
x
f (x) = e 2x
f (x) = 4e 3x
f (x) = e
2 x+3
f (x) = 4e 2 x+3 f (x) = 2e
3!4 x
f (x) = ln x f (x) = ln 2x Niet nodig 1
2 1
f (x) =
•2 =
= 2x
2x x
1
2 4
f ' (x) = 4 • • 2 = 4 •
= 2x
2x x
1
2
8
f ' (x) = 4 •
•2 = 4•
=
2x !1
2x !1 2x !1
1
1
1
f ' (x) =
•!1 = !
=
e! x
e! x x!e
Niet nodig '
f (x) = 4 ln 2x f (x) = 4 ln(2x !1) f (x) = ln(e ! x) f (x) = ln x ! e Niet nodig Niet Nodig Niet nodig Niet nodig f (x) = ln x ! e x Niet nodig 1
f (x) = x
F(x) = ln | x | +c 1
f (x) =
x+2
3
f (x) =
x+2
F(x) = ln | x + 2 | +c F(x) = 3ln | x + 2 | +c f (x) =
3
2 ! 4x
f !(x) = "1•
f (x) =
!3
4x ! 2
f !(x) = "1•
3
(2 " 4x )
2
"3
( 4x " 2)
2
•"4 =
•4 =
12
(2 " 4x)2
F(x) = 3ln | 2 ! 4x |•
1
3
+ c = ! ln | 2 ! 4x | +c !4
4
1
3
F(x) = !3ln | 4x ! 2 |• + c = ! ln | 4x ! 2 | +c 4
4
12
(4x " 2)2
f (x) = sin x f (x) = sin 2x f (x) = sin(2x + 3) f (x) = sin 3x + 2 1
f (x) = sin(2x + ! ) 3
1
f (x) = sin( ! ! 2x) 3
f (x) = cos x f (x) = cos2x f (x) = cos(2x + 3) !"
!
= −2cos ( − 2!) !"
3
sin
!
!
!
! − 2! !" = ! cos(! ! − 2!) + ! 1
cos 2! !" = sin 2! + ! 2
f (x) = cos3x + 2 !
(cos 3! + 2) !" = ! sin 3x +2x+c !
1
f (x) = cos(2x + ! ) 3
1
f (x) = cos( ! ! 2x) 3
!"
!"
f (x) = 3 x
f (x) = 3x + 4 f (x) = 452 x = 2025 x !"
!"
f (x) = 2 log x f (x) = 3 log x !
!
= −2 ∗ − sin ! ! − 2! = 2sin (! ! − 2!) !"
= ln 3 ∗ 3! !"
!"
= ln 3 ∗ 3! !"
= ln 2025 ∗ 2025! !"
1 1
1
=
∗ =
!" ln 2 ! ! ∗ ln 2
1
1
1
cos ! − 2! !" = − sin
− 2! + ! 3
2
3!
3! !" = f (x) = log(x + 3) f (x) = log(3x + 2) f (x) = log(x 2 + 3) 2x + 5
x!4
4x ! 2
f (x) =
2x ! 2
!!
(3! + 4 )!" = !" ! + 4! + ! 2025!
2025! !" = + ! ln 2025
f (x) = 3 log(x + 2) f (x) =
3!
+ ! ln 3
!5x +1
f (x) =
x+2
f (x) = (2x +1)e x f (x) = (2x +1)e3x f (x) = e x (1! x 2 ) f (x) = e x ln x f (x) = (x ! e)ln(e ! x) x2
ex
ln x
f (x) = x e
f (x) = (x ! 3)(x + 4) 2
f (x) =