Pertanyaan

Diketahui f ( x ) = sin x − cos x sin x , turunan dari f ( x ) adalah f ( x ) = ... .

Diketahui $f (x) = \frac{sin x}{sin x - cos x}$ , turunan dari $f (x)$ adalah $f (x) = ... .$

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Jawaban terverifikasi

Jawaban

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f apostrophe left parenthesis x right parenthesis equals negative 1 over open parentheses sin space x minus cos space x close parentheses squared

Pembahasan

Diketahui Misal dan maka dan Dengan demikian sebagai berikut. Jadi, .

Diketahui $f left parenthesis x right parenthesis equals fraction numerator sin space x over denominator sin space x minus cos space x end fraction$

Misal u left parenthesis x right parenthesis equals sin space x dan v open parentheses x close parentheses equals sin space x minus cos space x

maka u apostrophe left parenthesis x right parenthesis equals cos space x dan v apostrophe left parenthesis x right parenthesis equals cos space x plus sin space x

Dengan demikian f apostrophe open parentheses x close parentheses sebagai berikut.

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

Jadi, f apostrophe left parenthesis x right parenthesis equals negative 1 over open parentheses sin space x minus cos space x close parentheses squared .