Kapittel 1 Algebra

8 Oppgåver – Derivasjon Repetisjonskurs 2011
3.3 Logaritmer og eksponentialfunksjonen
Finn f ′ (x).
a) f (x) = x 2 + ln 3x
g) f (x) = e −x
m) f (x) = e x2 −1
e) f (x) = 2 + ln x − 1 2 x k) f (x) = x 0,5
f) f (x) = 2e x l) f (x) = e 2x+1 q) f (x) = 1 + x2 + x 6,7
x
b) f (x) = 2 + x + x 2 + ln x
c) f (x) = ln(kx)
d) f (x) = x − ln x
h) f (x) = e 2x
i) f (x) = e −3x
j) f (x) = x 1,5
n) f (x) = e √ x
o) f (x) = x 2 + ln x + e x2
p) f (x) = 2x 2,2 + 3x 2,7
3.4 Brøken 1 x n
Finn f ′ (x).
a) f (x) = − 1 e) f (x) = 3
h) f (x) =
x
2x
b) f (x) = x + 2 x
c) f (x) = x 2 − 2x − 3 f) f (x) = 1 x + 1
2x
x
d) f (x) = x 2 − 1 x 2 g) f (x) = 1 x (x − 1) j) f (x) =
1
(x + 1) 2
i) f (x) = 2 x + 1
x 3 − 1
1
√ x + 1
3.5 Produktregelen
Finn f ′ (x).
d) f (x) = xe −x
a) f (x) = x 2 e x
c) f (x) = (1 − x)e x f) f (x) = x ln(2x)
b) f (x) = 2x ln x
e) f (x) = x 2 e 2x
g) f (x) = e x ln x
3.6 Brøkfunksjonar
Finn f ′ (x).
a) f (x) = x + 1
x
b) f (x) = x − 1
x
c) f (x) = x
x − 1
d) f (x) = 2x
2x + 1
e) f (x) = x − 1
x − 2
f) f (x) = x 2 − 5
x − 5
g) f (x) = x + 1
x − 2
h) f (x) = 2 − x
1 − 2x
i) f (x) = x e x
j) f (x) = x
ln x