Samenvatting Wiskunde B / 5 vwo / deel leerboek

Wiskunde B
Hoofdstuk 11 en 12

Afgeleide Overzicht
f’(x) = rcf
finv is de inverse van f ​ dus ipv y = …. dan x = …
VERGEET PRODUCT, QUOTIENT OF KETTINGREGEL NIET
f(x) = a f’(x) = 0

f(x) = ax f’(x) = a
1
f(x) = 𝑥 f’(x) =
2 𝑥


f(x) = axn f’(x) = a * nxn-1

f(x) = c * g(x) f’(x) = c * g’(x)

s(x) = f(x) + g(x) s’(x) = f’(x) + g’(x) somregel

v(x) = f(x) - g(x) v’(x) = f’(x) - g’(x) verschilregel

p(x) = f(x) * g(x) p’(x) = f’(x) * g(x) + f(x) * g’(x) productregel

𝑡(𝑥) 𝑛(𝑥) * 𝑡'(𝑥) − 𝑡(𝑥) * 𝑛'(𝑥) quotientregel
q(x) = 𝑛(𝑥) q(x) =
(𝑛(𝑥))
2
nat min tan (natte tanja)

f(x) = u(v(x)) f’(x) = u’(v(x)) * v’(x) kettingregel

f(x) = ex. ​ f’(x) = ex e macht

f(x) = gx f’(x) = gx · ln(g)

f(x) = ln(x) f’(x) =
1
𝑥




f(x) = glog(x) f’(x) =
1
𝑥𝑙𝑛(𝑔)


f(x) = sin(x) f’(x) = cos(x)

f(x) = cos(x) f’(x) = -sin(x)

f(x) = tan(x) f’(x) =
1
2 = 1 + tan2(x)
𝑐𝑜𝑠 (𝑥)

, f(x) = axn F(x) = 𝑎 ·
1 𝑛+1
𝑥 + 𝑐 met n≠1
𝑛+1


f(x) = gx 𝑔
𝑥
F(x) = 𝑙𝑛(𝑔)
+𝑐

f(x) = ex. ​ F(x) = ex + c

f(x) =
1 F(x) = ln|x| + c
𝑥


f(x) = ln(x) F(x) = xln(x) - x + c

f(x) = glog(x) F(x) =
1
(xln(x) - x) + c
𝑙𝑛(𝑔)


f(x) = sin(x) F(x) = -cos(x) + c

f(x) = cos(x) F(x) = sin(x) + c

Integralen:
𝑏
𝑏
∫ 𝑓(𝑥)𝑑𝑥 = [𝐹(𝑥)] 𝑎
= 𝐹(𝑏) − 𝐹(𝑎)
𝑎
1
De primitieven van f(ax + b) zijn 𝑎
F(ax + b) + c


Overig;
bij een lijn y(x) = a(x - p)2 + q is de top (p, q)