Pertanyaan

Jika f ( x ) = − sin x 1 + cos x , maka d x df = ...

Jika $f (x) = \frac{1 + cos x}{- sin x}$ , maka $\frac{df}{d x} = ...$

$fraction numerator 1 plus cos x over denominator sin squared x end fraction$
$fraction numerator sin squared x plus cos squared x plus cos x over denominator negative sin squared x end fraction$
$fraction numerator sin squared x plus cos squared x plus cos x over denominator sin squared x end fraction$
$fraction numerator sin squared x minus cos squared x minus cos x over denominator sin squared x end fraction$

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Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat aturan berikut. Maka, Jadi turunan dari adalah . Oleh karena itu, jawaban yang benar adalah C.

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses fraction numerator 1 plus cos open parentheses x close parentheses over denominator negative sin open parentheses x close parentheses end fraction close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses negative fraction numerator 1 plus cos open parentheses x close parentheses over denominator sin open parentheses x close parentheses end fraction close parentheses end cell row blank equals cell negative fraction numerator d over denominator d x end fraction open parentheses fraction numerator 1 plus cos open parentheses x close parentheses over denominator sin open parentheses x close parentheses end fraction close parentheses end cell end table$

Ingat aturan berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f over g close parentheses to the power of apostrophe end cell equals cell fraction numerator f thin space apostrophe times g minus g apostrophe times f over denominator g squared end fraction end cell row f equals cell 1 plus cos left parenthesis x right parenthesis end cell row g equals cell sin left parenthesis x right parenthesis end cell end table$

Maka,

$begin mathsize 12px style negative fraction numerator d over denominator d x end fraction open parentheses fraction numerator 1 plus cos open parentheses x close parentheses over denominator sin open parentheses x close parentheses end fraction close parentheses equals negative fraction numerator fraction numerator d over denominator d x end fraction open parentheses 1 plus cos open parentheses x close parentheses close parentheses sin open parentheses x close parentheses minus fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses close parentheses open parentheses 1 plus cos open parentheses x close parentheses close parentheses over denominator open parentheses sin open parentheses x close parentheses close parentheses squared end fraction equals negative open parentheses fraction numerator open parentheses 0 minus sin left parenthesis x right parenthesis close parentheses sin open parentheses x close parentheses minus left parenthesis cos x right parenthesis open parentheses 1 plus cos open parentheses x close parentheses close parentheses over denominator open parentheses sin open parentheses x close parentheses close parentheses squared end fraction close parentheses equals negative open parentheses fraction numerator open parentheses negative sin left parenthesis x right parenthesis close parentheses sin open parentheses x close parentheses minus left parenthesis cos x right parenthesis open parentheses 1 plus cos open parentheses x close parentheses close parentheses over denominator open parentheses sin open parentheses x close parentheses close parentheses squared end fraction close parentheses equals negative open parentheses fraction numerator negative sin squared open parentheses x close parentheses minus cos open parentheses x close parentheses open parentheses 1 plus cos open parentheses x close parentheses close parentheses over denominator sin squared open parentheses x close parentheses end fraction close parentheses equals negative open parentheses fraction numerator negative sin squared open parentheses x close parentheses minus cos open parentheses x close parentheses minus cos squared left parenthesis x right parenthesis over denominator sin squared open parentheses x close parentheses end fraction close parentheses equals negative open parentheses fraction numerator negative sin squared open parentheses x close parentheses minus cos squared left parenthesis x right parenthesis minus cos open parentheses x close parentheses over denominator sin squared open parentheses x close parentheses end fraction close parentheses equals fraction numerator sin squared left parenthesis x right parenthesis plus cos squared left parenthesis x right parenthesis plus cos left parenthesis x right parenthesis over denominator negative sin squared left parenthesis x right parenthesis end fraction end style$

Jadi turunan dari $f left parenthesis x right parenthesis equals fraction numerator 1 plus cos space x over denominator negative sin space x end fraction$ adalah $fraction numerator sin squared x plus cos squared x plus cos x over denominator negative sin squared x end fraction$ .

Oleh karena itu, jawaban yang benar adalah C.