Pertanyaan

Turunan dari fungsi g ( t ) = 2 − sin 3 t 2 + cos 3 t adalah ....

Turunan dari fungsi $g (t) = \frac{2 + cos 3 t}{2 - sin 3 t}$ adalah ....

$begin mathsize 14px style fraction numerator 6 space sin space 3 straight t plus 6 space cos space 3 straight t minus 3 over denominator left parenthesis 2 minus sin space 3 straight t right parenthesis squared end fraction end style$
$begin mathsize 14px style fraction numerator negative 6 space sin space 3 straight t plus 6 space cos space 3 straight t plus 3 over denominator left parenthesis 2 minus sin space 3 straight t right parenthesis squared end fraction end style$
$begin mathsize 14px style fraction numerator 6 space sin space 3 straight t minus 6 space cos space 3 straight t plus 3 over denominator left parenthesis 2 minus sin space 3 straight t right parenthesis squared end fraction end style$

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Klaim

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Misal dan ,maka dan Ingat bahwa jika ,maka Perhatikan bahwa , sehingga Jadi, jawaban yang tepat adalah D.

Misal dan , maka dan

Ingat bahwa jika $begin mathsize 14px style straight g left parenthesis straight t right parenthesis equals fraction numerator straight u left parenthesis straight t right parenthesis over denominator straight v left parenthesis straight t right parenthesis end fraction end style$ , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight g to the power of apostrophe left parenthesis straight t right parenthesis end cell equals cell fraction numerator straight u to the power of apostrophe left parenthesis straight t right parenthesis times straight v left parenthesis straight t right parenthesis minus straight u left parenthesis straight t right parenthesis times straight v to the power of apostrophe left parenthesis straight t right parenthesis over denominator left parenthesis straight v left parenthesis straight t right parenthesis right parenthesis squared end fraction end cell row blank equals cell fraction numerator left parenthesis negative 3 space sin space 3 straight t right parenthesis times left parenthesis 2 minus sin space 3 straight t right parenthesis minus left parenthesis 2 plus cos space 3 straight t right parenthesis times left parenthesis negative 3 space cos space 3 straight t right parenthesis over denominator left parenthesis 2 minus sin space 3 straight t right parenthesis squared end fraction end cell row blank equals cell fraction numerator negative 6 space sin space 3 straight t plus 3 space sin squared space 3 straight t minus left parenthesis negative 6 space cos space 3 straight t minus 3 space cos squared space 3 straight t right parenthesis over denominator left parenthesis 2 minus sin space 3 straight t right parenthesis squared end fraction end cell row blank equals cell fraction numerator negative 6 space sin space 3 straight t plus 3 space sin squared space 3 straight t plus 6 space cos space 3 straight t plus 3 space cos squared space 3 straight t over denominator left parenthesis 2 minus sin space 3 straight t right parenthesis squared end fraction end cell row blank equals cell fraction numerator negative 6 space sin space 3 straight t plus 6 space cos space 3 straight t plus 3 open parentheses sin squared space 3 straight t plus cos squared space 3 straight t close parentheses over denominator left parenthesis 2 minus sin space 3 straight t right parenthesis squared end fraction end cell end table end style$

Perhatikan bahwa , sehingga

Jadi, jawaban yang tepat adalah D.