Pertanyaan

Turunan pertama dari fungsi g ( x ) = sin x + cos x sin x − cos x adalah...

Turunan pertama dari fungsi $g (x) = \frac{sin x - cos x}{sin x + cos x}$ adalah...

$fraction numerator 2 over denominator 1 plus cos space 2 x end fraction$
$fraction numerator 2 over denominator 1 plus sin space 2 x end fraction$
$fraction numerator 2 over denominator 1 minus sin space 2 x end fraction$
$fraction numerator 2 over denominator 1 minus cos space 2 x end fraction$

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Diketahui fungsi . Misalkan , maka Misalkan , maka Turunan dari adalah maka Jadi, jawaban yang benar adalah B.

Diketahui fungsi $g left parenthesis x right parenthesis equals fraction numerator sin space x minus cos space x over denominator sin space x plus cos space x end fraction$ .

Misalkan u equals sin space x minus space cos space x , maka

table attributes columnalign right center left columnspacing 0px end attributes row cell u apostrophe end cell equals cell cos space x minus left parenthesis negative sin space x right parenthesis end cell row blank equals cell cos plus sin space x end cell end table

Misalkan v equals sin space x plus cos space x , maka

v apostrophe equals cos space x minus sin space x

Turunan dari g left parenthesis x right parenthesis equals u over v adalah $g apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction$ maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell g apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator left parenthesis cos space x plus sin space x right parenthesis left parenthesis sin space x plus cos space x right parenthesis minus left parenthesis sin space x minus cos space x right parenthesis left parenthesis cos space x minus sin space x right parenthesis over denominator left parenthesis sin space x plus cos space x right parenthesis squared end fraction end cell row blank equals cell fraction numerator left parenthesis sin space x plus cos space x right parenthesis left parenthesis sin space x plus cos space x right parenthesis minus left parenthesis negative left parenthesis cos space x minus sin space x right parenthesis right parenthesis left parenthesis cos space x minus sin space x right parenthesis over denominator left parenthesis sin space x plus cos space x right parenthesis squared end fraction end cell row blank equals cell fraction numerator left parenthesis sin space x plus cos space x right parenthesis squared plus left parenthesis cos space x minus sin space x right parenthesis squared over denominator left parenthesis sin space x plus cos space x right parenthesis squared end fraction end cell row blank equals cell fraction numerator sin squared x plus 2 space sin space x space cos space x plus cos squared x plus cos squared x minus 2 space sin space x space cos space x plus sin squared x over denominator sin squared x plus 2 space sin space x space cos space x plus cos squared x end fraction end cell row blank equals cell fraction numerator left parenthesis sin squared x plus cos squared x right parenthesis plus left parenthesis sin squared x plus cos squared x right parenthesis over denominator left parenthesis sin squared x plus cos squared x right parenthesis plus 2 space sin space x space cos space x end fraction end cell row blank equals cell fraction numerator 1 plus 1 over denominator 1 plus sin space 2 x end fraction end cell row blank equals cell fraction numerator 2 over denominator 1 plus sin space 2 x end fraction end cell end table$

Jadi, jawaban yang benar adalah B.