Roboguru

Tentukan turunan kedua dari fungsi trigonometri berikut! b.y=sin2xcos3x

Pertanyaan

Tentukan turunan kedua dari fungsi trigonometri berikut!

b.y equals sin 2 x space cos 3 x

Pembahasan Soal:

Gunakan aturan berikut,

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f times g close parentheses apostrophe end cell equals cell f thin space apostrophe times g plus f times g apostrophe end cell row f equals cell sin open parentheses 2 x close parentheses end cell row g equals cell cos open parentheses 3 x close parentheses end cell row blank blank blank row blank blank cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses 2 x close parentheses cos open parentheses 3 x close parentheses close parentheses end cell row blank equals cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses 2 x close parentheses close parentheses cos open parentheses 3 x close parentheses plus fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 3 x close parentheses close parentheses sin open parentheses 2 x close parentheses end cell row blank equals cell cos open parentheses 2 x close parentheses fraction numerator d over denominator d x end fraction open parentheses 2 x close parentheses cos open parentheses 3 x close parentheses plus open parentheses negative sin open parentheses 3 x close parentheses fraction numerator d over denominator d x end fraction open parentheses 3 x close parentheses sin open parentheses 2 x close parentheses close parentheses end cell row blank equals cell cos open parentheses 2 x close parentheses cos open parentheses 3 x close parentheses times thin space 2 minus sin open parentheses 3 x close parentheses times thin space 3 times sin open parentheses 2 x close parentheses end cell row blank equals cell cos open parentheses 2 x close parentheses times thin space 2 cos open parentheses 3 x close parentheses plus open parentheses negative sin open parentheses 3 x close parentheses times thin space 3 close parentheses sin open parentheses 2 x close parentheses end cell row blank equals cell 2 cos open parentheses 2 x close parentheses cos open parentheses 3 x close parentheses minus 3 sin open parentheses 3 x close parentheses sin open parentheses 2 x close parentheses end cell end table end style

Kemudian cari turunan kedua,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator d over denominator d x end fraction open parentheses 2 cos open parentheses 2 x close parentheses cos open parentheses 3 x close parentheses minus 3 sin open parentheses 3 x close parentheses sin open parentheses 2 x close parentheses close parentheses end cell row blank equals cell fraction numerator d over denominator d x end fraction open parentheses 2 cos open parentheses 2 x close parentheses cos open parentheses 3 x close parentheses close parentheses minus fraction numerator d over denominator d x end fraction open parentheses 3 sin open parentheses 3 x close parentheses sin open parentheses 2 x close parentheses close parentheses end cell row blank equals cell 2 open parentheses fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 2 x close parentheses close parentheses cos open parentheses 3 x close parentheses plus fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 3 x close parentheses close parentheses cos open parentheses 2 x close parentheses close parentheses end cell row blank equals cell 2 open parentheses negative 2 sin open parentheses 2 x close parentheses cos open parentheses 3 x close parentheses minus 3 sin open parentheses 3 x close parentheses cos open parentheses 2 x close parentheses close parentheses end cell row blank blank cell negative 3 open parentheses cos open parentheses 3 x close parentheses times thin space 3 sin open parentheses 2 x close parentheses plus cos open parentheses 2 x close parentheses times thin space 2 sin open parentheses 3 x close parentheses close parentheses end cell row blank blank blank row blank equals cell negative 13 sin open parentheses 2 x close parentheses cos open parentheses 3 x close parentheses minus 12 cos open parentheses 2 x close parentheses sin open parentheses 3 x close parentheses end cell end table

 

Jadi, turunan kedua y equals sin 2 x space cos 3 x adalah y apostrophe apostrophe equals negative 13 sin open parentheses 2 x close parentheses cos open parentheses 3 x close parentheses minus 12 cos open parentheses 2 x close parentheses sin open parentheses 3 x close parentheses.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

G. Albiah

Mahasiswa/Alumni Universitas Galuh Ciamis

Terakhir diupdate 07 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Jika y(x)=3x4+sin(2x)+cos(3x), tentukan !

Pembahasan Soal:

Diketahui y open parentheses x close parentheses equals 3 x to the power of 4 plus sin open parentheses 2 x close parentheses plus cos open parentheses 3 x close parentheses. Jika terdapat y equals sin open parentheses a x close parentheses space text maka end text space y apostrophe equals a cross times cos open parentheses a x close parentheses sedangkan jika y equals cos open parentheses a x close parentheses space text maka end text space y apostrophe equals a cross times negative sin open parentheses a x close parentheses sehingga turunan pertama fungsi f open parentheses x close parentheses spaceyaitu

table attributes columnalign right center left columnspacing 0px end attributes row cell y open parentheses x close parentheses end cell equals cell 3 x to the power of 4 plus sin open parentheses 2 x close parentheses plus cos open parentheses 3 x close parentheses end cell row cell y apostrophe open parentheses x close parentheses end cell equals cell 4 cross times 3 x to the power of 4 minus 1 end exponent plus 2 cross times cos open parentheses 2 x close parentheses plus 3 cross times open parentheses negative sin open parentheses 3 x close parentheses close parentheses end cell row cell y apostrophe open parentheses x close parentheses end cell equals cell 12 x cubed plus 2 cos open parentheses 2 x close parentheses minus 3 sin open parentheses 3 x close parentheses end cell end table


Jadi table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe open parentheses x close parentheses end cell equals cell 12 x cubed plus 2 cos open parentheses 2 x close parentheses minus 3 sin open parentheses 3 x close parentheses. end cell end table

0

Roboguru

Tentukan turunan dari fungsi-fungsi trigonometri berikut. a. f(x)=3sinx+5cosx

Pembahasan Soal:

Ingatlah!

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f plus-or-minus g close parentheses apostrophe end cell equals cell f thin space apostrophe plus-or-minus g apostrophe end cell row cell fraction numerator d over denominator d x end fraction open parentheses 3 sin open parentheses x close parentheses plus 5 cos open parentheses x close parentheses close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses 3 sin open parentheses x close parentheses close parentheses plus fraction numerator d over denominator d x end fraction open parentheses 5 cos open parentheses x close parentheses close parentheses end cell end table

Cari turunan dari fraction numerator d over denominator d x end fraction open parentheses 3 sin open parentheses x close parentheses close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses 3 sin open parentheses x close parentheses close parentheses end cell equals cell 3 fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses close parentheses end cell row blank equals cell 3 cos open parentheses x close parentheses end cell end table

Cari turunan dari fraction numerator d over denominator d x end fraction open parentheses 5 cos open parentheses x close parentheses close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses 5 cos open parentheses x close parentheses close parentheses end cell equals cell 5 fraction numerator d over denominator d x end fraction open parentheses cos open parentheses x close parentheses close parentheses end cell row blank equals cell 5 open parentheses negative sin open parentheses x close parentheses close parentheses end cell row blank equals cell negative 5 sin open parentheses x close parentheses end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f plus-or-minus g close parentheses apostrophe end cell equals cell f thin space apostrophe plus-or-minus g apostrophe end cell row cell fraction numerator d over denominator d x end fraction open parentheses 3 sin open parentheses x close parentheses plus 5 cos open parentheses x close parentheses close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses 3 sin open parentheses x close parentheses close parentheses plus fraction numerator d over denominator d x end fraction open parentheses 5 cos open parentheses x close parentheses close parentheses end cell row blank equals cell 3 cos open parentheses x close parentheses minus 5 sin open parentheses x close parentheses end cell end table
 


Jadi, turunan fungsi f left parenthesis x right parenthesis equals 3 space sin space x space plus space 5 space cos space x adalah f apostrophe left parenthesis x right parenthesis equals 3 cos open parentheses x close parentheses minus 5 sin open parentheses x close parentheses.

1

Roboguru

Tentukan turunan dari masing-masing fungsi berikut: a. g(x)=sinxcosx

Pembahasan Soal:

Ingat aturan berikut!

open parentheses f times g close parentheses apostrophe equals f apostrophe g plus f. g apostrophe

dengan :

table attributes columnalign right center left columnspacing 0px end attributes row f equals cell sin space x end cell row g equals cell cos space x end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses close parentheses end cell equals cell cos space x end cell row cell fraction numerator d over denominator d x end fraction open parentheses cos open parentheses x close parentheses close parentheses end cell equals cell negative sin space x end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction sin space x space cos space x end cell equals cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses close parentheses cos open parentheses x close parentheses plus fraction numerator d over denominator d x end fraction open parentheses cos open parentheses x close parentheses close parentheses sin open parentheses x close parentheses end cell row blank equals cell cos open parentheses x close parentheses cos open parentheses x close parentheses plus open parentheses negative sin open parentheses x close parentheses close parentheses sin open parentheses x close parentheses end cell row blank equals cell cos squared open parentheses x close parentheses minus sin squared left parenthesis x right parenthesis end cell row blank equals cell cos space 2 x end cell end table
 


Jadi,   turunan dari straight g left parenthesis x right parenthesis equals sin space x space cos space x adalah g apostrophe left parenthesis x right parenthesis equals cos space 2 x.

0

Roboguru

Diketahui fungsi f(x)=sinxcos2x nilai dari f(6π​) adalah ...

Pembahasan Soal:

Cari turunan f left parenthesis x right parenthesis equals sin space x space cos space 2 x

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f times g close parentheses apostrophe end cell equals cell f thin space apostrophe times g plus f times g end cell row f equals cell sin left parenthesis x right parenthesis end cell row g equals cell cos left parenthesis 2 x right parenthesis end cell end table

Maka,

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses cos open parentheses 2 x close parentheses close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses close parentheses cos open parentheses 2 x close parentheses plus fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 2 x close parentheses close parentheses sin open parentheses x close parentheses end cell row blank equals cell cos open parentheses x close parentheses cos open parentheses 2 x close parentheses plus open parentheses negative sin open parentheses 2 x close parentheses fraction numerator d over denominator d x end fraction open parentheses 2 x close parentheses close parentheses end cell row blank equals cell cos open parentheses x close parentheses cos open parentheses 2 x close parentheses plus open parentheses negative sin open parentheses 2 x close parentheses times thin space 2 close parentheses end cell row blank equals cell cos open parentheses x close parentheses cos open parentheses 2 x close parentheses plus open parentheses negative sin open parentheses 2 x close parentheses times thin space 2 close parentheses sin open parentheses x close parentheses end cell row blank equals cell cos open parentheses x close parentheses cos open parentheses 2 x close parentheses minus sin open parentheses 2 x close parentheses times thin space 2 sin open parentheses x close parentheses end cell row blank equals cell cos open parentheses 2 x close parentheses cos open parentheses x close parentheses minus 2 times thin space 2 sin open parentheses x close parentheses cos open parentheses x close parentheses sin open parentheses x close parentheses end cell row blank equals cell cos open parentheses 2 x close parentheses cos open parentheses x close parentheses plus 4 open parentheses cos open parentheses 2 x close parentheses minus cos squared open parentheses x close parentheses close parentheses cos open parentheses x close parentheses end cell row blank equals cell cos open parentheses 2 x close parentheses cos open parentheses x close parentheses plus 4 cos open parentheses x close parentheses open parentheses cos open parentheses 2 x close parentheses minus cos squared open parentheses x close parentheses close parentheses end cell row blank equals cell cos open parentheses 2 x close parentheses cos open parentheses x close parentheses plus 4 cos open parentheses x close parentheses cos open parentheses 2 x close parentheses minus 4 cos cubed open parentheses x close parentheses end cell row blank equals cell negative 4 cos cubed open parentheses x close parentheses plus 5 cos open parentheses x close parentheses open parentheses 2 cos squared open parentheses x close parentheses minus 1 close parentheses end cell row blank equals cell negative 4 cos cubed open parentheses x close parentheses plus 10 cos cubed open parentheses x close parentheses minus 5 cos open parentheses x close parentheses end cell row blank equals cell equals 6 cos cubed open parentheses x close parentheses minus 5 cos open parentheses x close parentheses end cell row blank equals cell negative 5 cos open parentheses x close parentheses plus 6 cos cubed open parentheses x close parentheses end cell end table end style

Kemudian cari nilai f apostrophe open parentheses straight pi over 6 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses straight pi over 6 close parentheses end cell equals cell f apostrophe open parentheses 180 over 6 close parentheses end cell row blank equals cell f apostrophe open parentheses 30 close parentheses end cell row blank blank blank row cell negative 5 cos open parentheses x close parentheses plus 6 cos cubed open parentheses x close parentheses end cell equals cell negative 5 cos open parentheses 30 close parentheses plus 6 cos cubed open parentheses 30 close parentheses end cell row blank equals cell negative 5 times fraction numerator square root of 3 over denominator 2 end fraction plus 6 open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses cubed end cell row blank equals cell negative fraction numerator square root of 3 times thin space 5 over denominator 2 end fraction plus 6 times fraction numerator 3 square root of 3 over denominator 2 cubed end fraction end cell row blank equals cell negative fraction numerator square root of 3 times thin space 5 over denominator 2 end fraction plus fraction numerator 3 square root of 3 times thin space 6 over denominator 2 cubed end fraction end cell row blank equals cell negative fraction numerator square root of 3 times thin space 5 over denominator 2 end fraction plus fraction numerator 18 square root of 3 over denominator 2 cubed end fraction end cell row blank equals cell negative fraction numerator square root of 3 times thin space 5 over denominator 2 end fraction plus fraction numerator 3 squared times thin space 2 square root of 3 over denominator 2 cubed end fraction end cell row blank equals cell negative fraction numerator square root of 3 times thin space 5 over denominator 2 end fraction plus fraction numerator 9 square root of 3 over denominator 2 squared end fraction end cell row blank equals cell negative fraction numerator 5 square root of 3 over denominator 2 end fraction plus fraction numerator 9 square root of 3 over denominator 4 end fraction end cell row blank equals cell negative fraction numerator 10 square root of 3 over denominator 4 end fraction plus fraction numerator 9 square root of 3 over denominator 4 end fraction end cell row blank equals cell negative 1 fourth square root of 3 end cell end table


Jadi, nilai dari f apostrophe open parentheses straight pi over 6 close parentheses adalah negative 1 fourth square root of 3.


Oleh karena itu, jawaban yang benar adalahh B.

0

Roboguru

Tentukan turunan kedua dari fungsi trigonometri berikut! a.y=3sin3xcos3x

Pembahasan Soal:

Turunan pertama,

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f times g close parentheses apostrophe end cell equals cell f thin space apostrophe times g plus f times g apostrophe end cell row f equals cell sin open parentheses 3 x close parentheses comma thin space g equals cos open parentheses 3 x close parentheses end cell row blank blank cell fraction numerator d over denominator d x end fraction open parentheses 3 sin open parentheses 3 x close parentheses cos open parentheses 3 x close parentheses close parentheses end cell row blank equals cell 3 open parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses 3 x close parentheses close parentheses cos open parentheses 3 x close parentheses plus fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 3 x close parentheses close parentheses sin open parentheses 3 x close parentheses close parentheses end cell row blank equals cell 3 open square brackets cos open parentheses 3 x close parentheses fraction numerator d over denominator d x end fraction open parentheses 3 x close parentheses open parentheses cos open parentheses 3 x close parentheses close parentheses plus open parentheses negative sin open parentheses 3 x close parentheses fraction numerator d over denominator d x end fraction open parentheses 3 x close parentheses sin open parentheses 3 x close parentheses close parentheses close square brackets end cell row blank equals cell 3 open square brackets cos open parentheses 3 x close parentheses times thin space 3 times cos open parentheses 3 x close parentheses close square brackets plus open parentheses negative sin open parentheses 3 x close parentheses times thin space 3 times sin open parentheses 3 x close parentheses close parentheses end cell row blank equals cell 3 open parentheses cos open parentheses 3 x close parentheses times thin space 3 cos open parentheses 3 x close parentheses minus sin open parentheses 3 x close parentheses times thin space 3 sin open parentheses 3 x close parentheses close parentheses end cell row blank equals cell 3 open parentheses 3 cos squared open parentheses 3 x close parentheses minus 3 sin squared open parentheses 3 x close parentheses close parentheses end cell row blank equals cell 9 cos open parentheses 2 times thin space 3 x close parentheses end cell row blank equals cell 9 cos open parentheses 6 x close parentheses end cell end table end style

Turunan kedua,

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses 9 c o s 6 x close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses 9 c o s 6 x close parentheses end cell row blank equals cell 9 fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 6 x close parentheses close parentheses end cell row blank equals cell 9 times negative sin open parentheses 6 x close parentheses fraction numerator d over denominator d x end fraction open parentheses 6 x close parentheses end cell row blank equals cell 9 times negative sin open parentheses 6 x close parentheses 6 end cell row blank equals cell negative 54 sin open parentheses 6 x close parentheses end cell end table

 


Jadi, turunan kedua y equals 3 sin 3 x space cos 3 x adalah y apostrophe apostrophe equals 54 sin open parentheses 6 x close parentheses.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved