Pertanyaan

Diketahui fungsi f dinyatakan oleh f ( x ) = sec x sin x . Turunan pertama dari f yaitu f'. Tentukan : b. nilai f ( 6 π )

Diketahui fungsi f dinyatakan oleh $f (x) = \frac{sin x}{sec x}$ . Turunan pertama dari f yaitu f'. Tentukan :

b. nilai $f (\frac{π}{6})$

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Pembahasan

Ingat aturan pembagian turunan fungsi trigonometri : Sehingga pada fungsi diketahui : Maka, turunan fungsinya menjadi : Maka,nilai .

Ingat aturan pembagian turunan fungsi trigonometri :

$f left parenthesis x right parenthesis equals u over v f apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction$

Sehingga pada fungsi $straight f left parenthesis x right parenthesis equals fraction numerator sin space x over denominator sec space x end fraction$ diketahui :

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell sin space x end cell row cell u apostrophe end cell equals cell cos space x end cell row v equals cell sec space x end cell row cell v apostrophe end cell equals cell sec space x. tan space x end cell end table

Maka, turunan fungsinya menjadi :

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator u apostrophe v minus v apostrophe u over denominator v squared end fraction end cell row blank equals cell fraction numerator cos space x times sec space x minus sec space x times tan space x times sin space x over denominator open parentheses sec space x close parentheses squared end fraction end cell row cell f apostrophe left parenthesis straight pi over 6 right parenthesis end cell equals cell fraction numerator fraction numerator square root of 3 over denominator 2 end fraction times fraction numerator 2 over denominator square root of 3 end fraction minus fraction numerator 2 over denominator square root of 3 end fraction times fraction numerator square root of 3 over denominator 3 end fraction times 1 half over denominator open parentheses fraction numerator 2 over denominator square root of 3 end fraction close parentheses squared end fraction end cell row blank equals cell fraction numerator fraction numerator up diagonal strike square root of 3 end strike over denominator 2 end fraction times fraction numerator 2 over denominator down diagonal strike square root of 3 end strike end fraction minus fraction numerator 2 over denominator up diagonal strike square root of 3 end strike end fraction times fraction numerator down diagonal strike square root of 3 end strike over denominator 3 end fraction times 1 half over denominator 4 over 3 end fraction end cell row blank equals cell fraction numerator 2 over 2 minus 2 over 6 over denominator 4 over 3 end fraction end cell row blank equals cell fraction numerator 6 over 6 minus 2 over 6 over denominator 4 over 3 end fraction end cell row blank equals cell fraction numerator 4 over 6 over denominator 4 over 3 end fraction end cell row blank equals cell 4 over 6 cross times 3 over 4 end cell row blank equals cell 3 over 6 end cell row blank equals cell 1 half end cell end table$

Maka, nilai straight f apostrophe open parentheses straight pi over 6 close parentheses equals 1 half .