0
0/12
13
Differentialrechnung
0/12/2
13.2
Ableitungsregeln
0/12/2/5
13.2.5
Kettenregel
0/12/2/5/0
Beispiel 13 - 1:
y
=
sin
(
3
x
+
4
)
y
=
f
(
x
)
S
u
b
s
t
i
t
u
t
i
o
n
→
u
=
u
(
x
)
y
=
f
(
u
)
u
=
u
(
x
)
Innere Funktion
y
=
f
(
u
)
Äußere Funktion
y
=
f
(
u
)
=
f
(
u
(
x
)
)
=
f
(
x
)
y
′
=
d
y
d
x
=
d
y
d
u
⋅
d
u
d
x
u
=
3
x
+
4
d
u
d
x
=
3
F
(
u
)
=
sin
(
u
)
d
y
d
u
=
cos
(
u
)
y
′
=
d
y
d
u
⋅
d
u
d
x
=
cos
(
u
)
⋅
3
=
3
cos
(
3
x
+
4
)
.
.
d
y
d
x
=
lim
Δ
x
→
0
Δ
y
Δ
x
=
lim
Δ
x
→
0
d
y
d
u
⋅
d
u
d
x
=
lim
Δ
x
→
0
Δ
y
Δ
u
⋅
lim
Δ
x
→
0
Δ
u
Δ
x
=
Δ
y
Δ
u
⋅
Δ
u
Δ
x
.