Transcript 07-Derivatif FUNGSI TRIGONOMETRI

ITK-121
KALKULUS I
3 SKS
Dicky Dermawan
www.dickydermawan.890m.com
TURUNAN FUNGSI
TRIGONOMETRI
Teorema 1:
d
(sin x)  cos x atau
dx
Teorema 2:
d
cos x    sin x
dx
(sin x) '  cos x
Teorema 3a:
d
(sec x)  sec x  tan x
dx
Teorema 3b:
d
(csc x) '   csc x  cot x
dx
Teorema 4:
d
(tan x) '  sec 2 x
dx
dan
d
(cot x)   csc 2 x
dx
Contoh-contoh
1. d ( x  sin x  cos x)
dx
2.
d
(sin 2 x)
dx
3.
d 3
( x sec x )
dx
4
d  csc x 


dx  x 
Soal-soal
1.
2.
3.
2
x sin x
3
x cos x
1  sin x
cos x
4. 1  sin x
cos x
5. 1  3 sec x
tan x
6. x 3 sec x
7. csc x
3
x
Soal-soal
8.
sin x  tan x
9.
x  cos x  cot x 13. cos x  x  sin x
2
cot x
10.
2
1 x
11.
12. sin x  x  cos x
x
1  sec x
14.
2 x  sin x  2 cos x  x 2  cos x
15
3x 2 sin x  6 sin x  x 3 cos x  6 x cos x
23
sin x  cos2 x
16
tan(x )  x
24
( x  sin x)(x  cos x)
17
2 x  cos x  2 sin x  x sin x
25
sin 2 x
1  cos 2 x
18
(3x 2  6) cos x  ( x 2  6) sin x
26
1  cos x
x  sin x
27
x  tan x
28
x 2 sin x
cos x
2
19
sin x
sin x  cos x
20
sin x  cos x
21
22
2
x2 1
x  sin x
x 2 sin x
x 1
2