Wiskunde: Rekenregels
1. Dc = 0
F(x) = c
lim f ( x +∆ x )−f (x )
F’(x) = ∆x →0
∆x
lim c−c
= ∆x →0
∆x
=0
2. Dx = 1
F(x) = x
lim f ( x +∆ x )−f (x )
F’(x) = ∆x →0
∆x
lim x+ ∆ x−x
= ∆x →0
∆x
lim ∆ x
= ∆x →0
∆x
=1
3. Dx2 = 2x
F(x) = x2
lim f ( x +∆ x )−f (x )
F’(x) = ∆x →0
∆x
lim ( x +∆ x )−x
2 2
= ∆x →0
∆x
2 2 2
lim x +2 x ∆ x+ ∆ x −x
= ∆x →0
∆x
lim
= ∆ x→ 0 2 x+ ∆ x
= 2x
4. Dx3 = 3x2
F(x) = x3
F’(x) = ∆lim
x→ 0
¿¿
lim x 3+3 x 2 ∆ x+ 3 x ∆ x 2+ ∆ x 3−x 3
= ∆x →0
∆x
2 2
= lim 3 x + 3 x ∆ x +∆ x
∆ x→ 0
= 3x2
1. Dc = 0
F(x) = c
lim f ( x +∆ x )−f (x )
F’(x) = ∆x →0
∆x
lim c−c
= ∆x →0
∆x
=0
2. Dx = 1
F(x) = x
lim f ( x +∆ x )−f (x )
F’(x) = ∆x →0
∆x
lim x+ ∆ x−x
= ∆x →0
∆x
lim ∆ x
= ∆x →0
∆x
=1
3. Dx2 = 2x
F(x) = x2
lim f ( x +∆ x )−f (x )
F’(x) = ∆x →0
∆x
lim ( x +∆ x )−x
2 2
= ∆x →0
∆x
2 2 2
lim x +2 x ∆ x+ ∆ x −x
= ∆x →0
∆x
lim
= ∆ x→ 0 2 x+ ∆ x
= 2x
4. Dx3 = 3x2
F(x) = x3
F’(x) = ∆lim
x→ 0
¿¿
lim x 3+3 x 2 ∆ x+ 3 x ∆ x 2+ ∆ x 3−x 3
= ∆x →0
∆x
2 2
= lim 3 x + 3 x ∆ x +∆ x
∆ x→ 0
= 3x2
