1. TURUNAN / DEFERENSIAL

3. AdaptjikaHal.: 3 adalahi dengan Judul Halaman
Turunan atau deferensial
Standar Kompetensi
Menggunakan konsep limit fungsi dan turunan fungsi dalam
pemecahan masalah.
Indikator
Menentukan berbagai turunan fungsi trigonometri
Kompetensi Dasar
Menggunakan konsep dan aturan turunan dalam perhitungan turunan
fungsi

4. Adaptjika
Competence Standard
Using function limit concept and function differential in problem
solving.
Indicator
Define the kinds of differential in trigonometric function
Basic Competence
Using the concept and rules of differential in counting function
differential
DIFFERENTIAL

5. Adaptjika
TURUNAN / DEFERENSIAL
1. Jika , maka
2. Jika , maka
3. Jika , maka
xy sin=
xy cos= x
dx
dy
y sin' −==
x
dx
dy
y cos' ==
xy tan= x
dx
dy
y 2
sec' ==
Rumus – rumus turunan fungsi trigonometri

6. Adaptjika
The Formula of Differential in Trigonometric Function
 1. If , then
 2. If , then
 3. If , then
xy cos= x
dx
dy
y sin' −==
xy sin= x
dx
dy
y cos' ==
xy tan= x
dx
dy
y 2
sec' ==

7. Adaptjika
Contoh 1
xxy sin2
=Carilah turunan fungsi trigonometri
Jawab
Misalkan
Maka,
xuxu 2'2
=→=
xvxv cos'sin =→=
''' uvvuy +=
))(cos())(sin2( 2
xxxx +=
xxxx cossin2 2
+=
TURUNAN / DEFERENSIAL

8. Adaptjika
Example 1
xxy sin2
=Find the differential of trigonometric function
Answer
For example
then,
xuxu 2'2
=→=
xvxv cos'sin =→=
''' uvvuy +=
))(cos())(sin2( 2
xxxx +=
xxxx cossin2 2
+=
DIFFERENTIAL

9. Adaptjika
Contoh 2
Jawab
xxxy 3sin6cos5sin −+=Carilah turunan fungsi trigonometri
)3)(cos3()6sin)(6(5cos)5(' xxxy −−+=
xxxy 3sin6cos5sin −+=
xxxy 3cos36sin65cos5' −−=⇒
TURUNAN / DEFERENSIAL

10. Adaptjika
xxxy 3sin6cos5sin −+=
Example 2
Find the differential of trigonometric function
Answer
)3)(cos3()6sin)(6(5cos)5(' xxxy −−+=
xxxy 3sin6cos5sin −+=
xxxy 3cos36sin65cos5' −−=⇒
DIFFERENTIAL

11. Adaptjika
Contoh 3
xy tan=Carilah turunan fungsi trigonometri
2
)(
''
'
v
uvvu
y
−
=
xuxu cos'sin =→=
xvxv sin'cos −=→=
Misalkan
TURUNAN / DEFERENSIAL
Jawab
x
x
xy
cos
sin
tan ==

12. Adaptjika
Example 3
xy tan=Find the differential of trigonometric function
Answer
x
x
xy
cos
sin
tan ==
xuxu cos'sin =→=
xvxv sin'cos −=→=
2
)(
''
'
v
uvvu
y
−
=
For example
DIFFERENTIAL

13. Adaptjika
2
)(cos
)sin)((sin))(cos(cos
x
xxxx −−
=
x
xx
2
22
cos
sincos +
=
xxx cos
1
.
cos
1
cos
1
2
==
xx sec.sec=
x2
sec=
Lanjutan
TURUNAN / DEFERENSIAL

14. Adaptjika
2
)(cos
)sin)((sin))(cos(cos
x
xxxx −−
=
x
xx
2
22
cos
sincos +
=
xxx cos
1
.
cos
1
cos
1
2
==
xx sec.sec=
x2
sec=
Continuation
DIFFERENTIAL