Kapittel 1 Algebra

8 Fasit – Derivasjon Repetisjonskurs 2011
a) f ′ (x) = 2x + 1 x
g) f ′ (x) = −e −x
m) f ′ (x) = 2xe x2 −1
f) f ′ (x) = 2e x l) f ′ (x) = 2e 2x+1 q) f ′ (x) = − 1 + 1 + 5, 7x4,7
x2 b) f ′ (x) = 1 + 2x + 1 h) f ′ (x) = 2e
x
n) f ′ (x) = 1
c) f ′ (x) = 1 i) f ′ 2 √ x e√ x
(x) = −3e −3x
x
d) f ′ (x) = 1 − 1 x
e) f ′ (x) = 1 x − 1 2
j) f ′ (x) = 1, 5x 0,5
k) f ′ (x) = 0, 5x −0,5
o) f ′ (x) = 2x + 1 x + 2xex2
p) f ′ (x) = 4, 4x 1,2 + 8, 1x 1,7
3.4 Brøken 1 x n
Finn f ′ (x).
a) f ′ (x) = 1 x 2
e) f ′ (x) = − 3
2x 2
h) f ′ 2
(x) = −
(x + 1) 3
b) f ′ (x) = 1 − 2 x 2
c) f ′ (x) = 2x − 2 + 3 f) f ′ (x) = − 1 x 2 − 1
i) f ′ (x) = − 2 2x 2
x 2 − 3x2
(x 3 − 1) 2
x 2
d) f ′ (x) = 2x + 2 x 3 g) f ′ (x) = − 1 j) f ′ 1
(x) = −
x 2 2( √ x + 1) 3
3.5 Produktregelen
d) f ′ (x) = e −x − xe −x
a) f ′ (x) = 2xe x + x 2 e x
c) f ′ (x) = −e x + (1 − x)e x f) f ′ (x) = ln(2x) + 1
b) f ′ (x) = 2 ln x + 2
e) f ′ (x) = 2xe 2x + 2x 2 e 2x
g) f ′ (x) = e x ln x + ex
x
3.6 Brøkfunksjonar
a) f ′ (x) = − 1 x 2
f) f ′ 5
(x) = 2x +
(x − 5) 2 j) f ′ (x) = ln x − 1
(ln x) 2
b) f ′ (x) = 1 x 2
g) f ′ 3
(x) = −
c) f ′ 1
(x − 2) 2 k) f ′ (x) = 1 − x ln x
xe x
(x) = −
(x − 1) 2
d) f ′ 2
h) f ′ 3
(x) =
(x) =
(2x + 1) 2
(1 − 2x) 2
l) f ′ (x) = e3x (3x − 1)
x 2
e) f ′ 1
(x) = 1 +
(x − 2) 2 i) f ′ (x) = ex − xe x
m) f ′ (x) = 2 ln x − 2
e 2x (ln x − x) 2