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Matematik 1
Matematik 2
Matematik 3
Matematik 4
Matematik 5
Matematik 1
Matematik 2
Matematik 3
Matematik 4
Matematik 5
1
Ma1
2
Ma2
3
Ma3
4
Ma4
5
Ma5
Hem
Derivata
Derivata
Formler från Matematik 3
Derivata
Ma3
Definition
f
′
(
a
)
=
lim
h
→
0
f
(
a
+
h
)
−
f
(
a
)
h
f'(a) = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}
f
′
(
a
)
=
lim
h
→
0
h
f
(
a
+
h
)
−
f
(
a
)
Ma3
Potensfunktion
d
d
x
(
x
n
)
=
n
x
n
−
1
\frac{d}{dx}(x^n) = nx^{n-1}
d
x
d
(
x
n
)
=
n
x
n
−
1
Ma3
1/x
d
d
x
(
1
x
)
=
−
1
x
2
\frac{d}{dx}\left(\frac{1}{x}\right) = -\frac{1}{x^2}
d
x
d
(
x
1
)
=
−
x
2
1
Ma3
Exponentialfunktion
d
d
x
(
a
x
)
=
a
x
ln
a
\frac{d}{dx}(a^x) = a^x \ln a
d
x
d
(
a
x
)
=
a
x
ln
a
Ma3
e^x
d
d
x
(
e
x
)
=
e
x
\frac{d}{dx}(e^x) = e^x
d
x
d
(
e
x
)
=
e
x
Ma3
e^(kx)
d
d
x
(
e
k
x
)
=
k
e
k
x
\frac{d}{dx}(e^{kx}) = ke^{kx}
d
x
d
(
e
k
x
)
=
k
e
k
x
Ma3
Konstant · funktion
d
d
x
(
k
⋅
f
(
x
)
)
=
k
⋅
f
′
(
x
)
\frac{d}{dx}(k \cdot f(x)) = k \cdot f'(x)
d
x
d
(
k
⋅
f
(
x
))
=
k
⋅
f
′
(
x
)
Ma3
Summa
d
d
x
(
f
(
x
)
+
g
(
x
)
)
=
f
′
(
x
)
+
g
′
(
x
)
\frac{d}{dx}(f(x) + g(x)) = f'(x) + g'(x)
d
x
d
(
f
(
x
)
+
g
(
x
))
=
f
′
(
x
)
+
g
′
(
x
)