Pertanyaan

Diketahui fungsi f ( x ) = sin x cos 2 x nilai dari f ( 6 π ) adalah ...

Diketahui fungsi $f (x) = sin x cos 2 x$ nilai dari $f (\frac{π}{6})$ adalah ...

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Habis dalam

Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalahh B.

Pembahasan

Cari turunan Maka, Kemudian cari nilai Jadi,nilai dari adalah . Oleh karena itu, jawaban yang benar adalahh B.

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.