嗤捍 慵 /title> head>body bgcolor=#ffffff vlink

4MA1DF01bil
Wiederholung : Ableitungen
Wiederholung : Ableitungen
Die Ableitungen folgender Funktionen berehnen :
1.
f (x) =
1
sin(x)
2.
f (x) =
x
ln(x)
3.
f (x) =
(x − 1)3
(x + 1)2
4.
f (x) = e−x · cos(x)
5.
f (x) = x ln(x) − x
6.
f (x) =
7.
f (x) =
′
f (x) =
′
−x
f (x) = −e
9.
f (x) = sin(2x)
−x
· sin (x)
20x
′
f (x) = −
2
2x2 − 1
2x + 1
′
f (x) =
q
3
2
x2 + x + 1
′
f (x) = −5 (3 − x)
4
′
f (x) = 2 cos (2x)
10.
f (x) =
11.
f (x) = (3x2 + 4) (2x2 − 3x)
12.
f (x) = sin(2x) · cos(3x)
13.
f (x) = ln (3x5 )
14.
(3x − 2)2 − 1
f (x) =
3x − 2
15.
f (x) = 3x5 −
AK
(x + 1)3
· cos (x) − e
3·
f (x) = (3 − x)5
(x − 1)2 (x + 5)
′
x2 + x + 1
8.
ln2 (x)
f (x) = ln (x)
5
−1
√
7
ln (x) − 1
′
f (x) =
2x2
√
3
cos(x)
sin2 (x)
′
f (x) = −
x4
′
f (x) =
7·
5
6
7x3 3x2
+
− x + 17
6
4
′
5
f (x) = 12x (2x − 3)
5
4
2
3x + 4
3
4
√
7
x3
2
11x − 12x + 8x − 6
′
f (x) = 2 cos (2x) cos (3x) − 3 sin (2x) sin (3x)
5
′
f (x) =
′
f (x) =
′
x
3 9x2 − 12x + 5
(3x − 2)2
4
f (x) = 15x −
7x2
2
+
3x
2
−1
CdC 2014-2015
4MA1DF01bil
Wiederholung : Ableitungen
2x − 1
x
2 !
16.
f (x) = sin
17.
f (x) = ln(5x)
18.
f (x) = cos(x) sin2 (x) + 2
19.
−2
f (x) = √
3
x2
20.
f (x) = 2 sin(x) + cos(3x)
21.
x2
f (x) = ln
1−x
22.
f (x) =
4 − 3x
2x − 1
23.
f (x) =
1
x ln(x)
24.
f (x) = e5x
25.
f (x) = sin3 (4x)
26.
f (x) =
2 (2x − 1)
· cos
x3
2x−1
x
2 1
′
f (x) =
′
2
2
3
f (x) = sin (x) 2 cos (x) − sin (x) − 2
4
√
3
′
f (x) =
3·
x
= −3 sin (x)
=
x5
3x ·
4
√
3
x2
′
f (x) = 2 cos (x) − 3 sin (3x)
!
2−x
′
f (x) =
x (1 − x)
5
(2x−1)2
′
f (x) = −
′
f (x) = −
ln (x) + 1
x2 ln2 (x)
5x
′
f (x) = 5e
2
′
f (x) = 12 cos (4x) sin (4x)
q
(4x2 − 2x)3
′
f (x) = 3 · (4x − 1) ·
27.
f (x) = exp
28.
f (x) = x2 ex
p
4x2 − 2x
1
x
exp
1
x
′
f (x) = −
x2
′
x
f (x) = x (x + 2) e
√
3
f (x) = (1 +
30.
f (x) = (x2 + a2 )
31.
1
f (x) = √
4
x
32.
f (x) = ln (x2 − x)
x)
√ 2
1+ 3x
√
3 2
x
3
29.
AK
′
f (x) =
′
f (x) =
5
′
f (x) = 10x
′
f (x) = −
4·
1
√
4
x5
′
2
x +a
=−
f (x) =
2
4
1
√
4x · 4 x
2x − 1
x (x − 1)
CdC 2014-2015