Samenvatting Differentiëren

Differentiëren
f ( x)=ax → f ' (x)=a
n❑
f ( x)=ax ❑ → f ' (x)=nax ❑n−1
f ( x)=c ∗ g ( x) → f ' (x)=c ∗ g ' (x)

f ( x)=sin(x) → f ' (x)=cos(x )
f ( x)=cos(x ) → f ' (x)=−sin( x )
2
f ( x)=tan( x ) → f ' (x)=1+ tan ❑ (x)
❑




Somregel

s( x )=f ( x)+ g(x ) → s ' ( x )=f ' (x)+ g ' ( x)

vb.
s( x )=4 x❑3 +2 x → s '( x )=12 x❑2 +2

Productregel

p( x )=f ( x)∗ g(x ) → p ' (x )=f ' (x) ∗ g( x )+f ( x)∗ g '( x )

vb.
p( x )=4 x❑3❑∗ 2 x → p ' (x )=12 x ❑2 ∗ 2 x+ 4 x ❑3❑ ∗2
p ' (x )=32 x❑3
Quotiëntregel

t( x ) n (x) ∗t ' (x)−t(x )∗ n ' (x )
q ( x)= → q ' ( x)= 2
n ( x) (n ( x))❑

vb.
x ❑ −1
2
( x ❑2 +1)∗ 2 x−( x ❑2−1)∗2 x
q ( x)= → q ' ( x)= 2 2
x ❑2 +1 ( x ❑ +1)❑
4x
q ' ( x)= 2 2
( x ❑ +1)❑

Kettingregel

f ( x)=u( v( x)) → f ' (x)=u' ( v ( x))∗ v ' (x )

vb.
f ( x)=( x ❑2−5 x)❑4 → f ' (x)=4 ∗( x ❑2−5 x)❑3 ∗(2 x−5)
4
u( v)=v ❑
v=¿ x ❑2−5 x