TURUNAN / DEFERENSIAL
AdaptjikaHal.: 3 adalahi dengan Judul Halaman
Turunan atau deferensial
Standar Kompetensi
Menggunakan konsep limit fungsi ...
Adaptjika
Competence Standard
Using function limit concept and function differential in problem
solving.
Indicator
Define ...
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 ...
Adaptjika
The Formula of Differential in Trigonometric Function
 1. If , then
 2. If , then
 3. If , then
xy cos= x
dx
...
Adaptjika
Contoh 1
xxy sin2
=Carilah turunan fungsi trigonometri
Jawab
Misalkan
Maka,
xuxu 2'2
=→=
xvxv cos'sin =→=
''' uv...
Adaptjika
Example 1
xxy sin2
=Find the differential of trigonometric function
Answer
For example
then,
xuxu 2'2
=→=
xvxv c...
Adaptjika
Contoh 2
Jawab
xxxy 3sin6cos5sin −+=Carilah turunan fungsi trigonometri
)3)(cos3()6sin)(6(5cos)5(' xxxy −−+=
xxx...
Adaptjika
xxxy 3sin6cos5sin −+=
Example 2
Find the differential of trigonometric function
Answer
)3)(cos3()6sin)(6(5cos)5(...
Adaptjika
Contoh 3
xy tan=Carilah turunan fungsi trigonometri
2
)(
''
'
v
uvvu
y
−
=
xuxu cos'sin =→=
xvxv sin'cos −=→=
Mi...
Adaptjika
Example 3
xy tan=Find the differential of trigonometric function
Answer
x
x
xy
cos
sin
tan ==
xuxu cos'sin =→=
x...
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
se...
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
se...
Turunan trigonometri bilingual
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Turunan trigonometri bilingual

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Turunan trigonometri bilingual

  1. 1. TURUNAN / DEFERENSIAL
  2. 2. 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
  3. 3. 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
  4. 4. 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
  5. 5. 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' ==
  6. 6. 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
  7. 7. 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
  8. 8. Adaptjika Contoh 2 Jawab xxxy 3sin6cos5sin −+=Carilah turunan fungsi trigonometri )3)(cos3()6sin)(6(5cos)5(' xxxy −−+= xxxy 3sin6cos5sin −+= xxxy 3cos36sin65cos5' −−=⇒ TURUNAN / DEFERENSIAL
  9. 9. Adaptjika xxxy 3sin6cos5sin −+= Example 2 Find the differential of trigonometric function Answer )3)(cos3()6sin)(6(5cos)5(' xxxy −−+= xxxy 3sin6cos5sin −+= xxxy 3cos36sin65cos5' −−=⇒ DIFFERENTIAL
  10. 10. 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 ==
  11. 11. 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
  12. 12. 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
  13. 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= Continuation DIFFERENTIAL

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