turunan trigonometri bilingual

TURUNAN / DEFERENSIAL

AdaptjikaHal.: 3 adalahi dengan Judul Halaman Terkait

Turunan atau deferensial

Standar KompetensiMenggunakan konsep limit fungsi dan turunan fungsi dalam pemecahan masalah.

IndikatorMenentukan berbagai turunan fungsi trigonometri

Kompetensi Dasar

Menggunakan konsep dan aturan turunan dalam perhitungan turunan fungsi

Adaptjika

Competence StandardUsing function limit concept and function differential in problem solving.

IndicatorDefine the kinds of differential in trigonometric function

Basic Competence

Using the concept and rules of differential in counting function differential

DIFFERENTIAL

Adaptjika

TURUNAN / DEFERENSIAL

1. Jika , maka

2. Jika , maka

3. Jika , maka

xy sin

xy cos xdx

dyy sin'

xdx

dyy cos'

xy tan xdx

dyy 2sec'

Rumus – rumus turunan fungsi trigonometri

Adaptjika

The Formula of Differential in Trigonometric Function

1. If , then

2. If , then

3. If , then

xy cos xdx

dyy sin'

xy sin xdx

dyy cos'

xy tan xdx

dyy 2sec'

Adaptjika

Contoh 1

xxy sin2Carilah turunan fungsi trigonometri

Jawab

Misalkan

Maka,

xuxu 2'2 xvxv cos'sin

''' uvvuy ))(cos())(sin2( 2 xxxx xxxx cossin2 2

TURUNAN / DEFERENSIAL

Adaptjika

Example 1

xxy sin2Find the differential of trigonometric function

Answer

For example

then,

xuxu 2'2 xvxv cos'sin

''' uvvuy ))(cos())(sin2( 2 xxxx xxxx cossin2 2

DIFFERENTIAL

Adaptjika

Contoh 2

Jawab

xxxy 3sin6cos5sin Carilah turunan fungsi trigonometri

)3)(cos3()6sin)(6(5cos)5(' xxxy xxxy 3sin6cos5sin

xxxy 3cos36sin65cos5'

TURUNAN / DEFERENSIAL

Adaptjika

xxxy 3sin6cos5sin

Example 2

Find the differential of trigonometric function

Answer

)3)(cos3()6sin)(6(5cos)5(' xxxy xxxy 3sin6cos5sin

xxxy 3cos36sin65cos5'

DIFFERENTIAL

Adaptjika

Contoh 3

xy tanCarilah turunan fungsi trigonometri

2)(

'''

v

uvvuy

xuxu cos'sin

xvxv sin'cos

Misalkan

TURUNAN / DEFERENSIAL

Jawabx

xxycos

sintan

Adaptjika

Example 3

xy tanFind the differential of trigonometric function

Answerx

xxycos

sintan

xuxu cos'sin

xvxv sin'cos

2)(

'''

v

uvvuy

For example

DIFFERENTIAL

Adaptjika

2)(cos

)sin)((sin))(cos(cos

x

xxxx

x

xx2

22

cos

sincos

xxx cos

1.

cos

1

cos

12

xx sec.sec

x2sec

Lanjutan

TURUNAN / DEFERENSIAL

Adaptjika

2)(cos

)sin)((sin))(cos(cos

x

xxxx

x

xx2

22

cos

sincos

xxx cos

1.

cos

1

cos

12

xx sec.sec

x2sec

Continuation

DIFFERENTIAL