Pertanyaan

Tentukan turunan dari fungsi-fungsi trigonometri berikut. c. h ( x ) = x sin x x 2 + 1

Tentukan turunan dari fungsi-fungsi trigonometri berikut.

c. $h (x) = \frac{x ^{2} + 1}{x sin x}$

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G. Albiah

Master Teacher

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Jawaban terverifikasi

Jawaban

turunan dari adalah .

turunan dari $h left parenthesis x right parenthesis equals fraction numerator x squared plus 1 over denominator x space sin space x end fraction$ adalah $h apostrophe left parenthesis x right parenthesis equals fraction numerator x squared sin open parentheses x close parentheses minus sin open parentheses x close parentheses minus x cubed cos open parentheses x close parentheses minus x cos open parentheses x close parentheses over denominator x squared sin squared open parentheses x close parentheses end fraction$ .

Pembahasan

Ingatlah! Maka, Cari turunan Cari turunan Maka, Ingatlah aturan berikut, Maka, Sehingga, Jadi, turunan dari adalah .

Ingatlah!

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

Maka,

$fraction numerator d over denominator d x end fraction open parentheses fraction numerator x squared plus 1 over denominator x sin open parentheses x close parentheses end fraction close parentheses equals fraction numerator fraction numerator d over denominator d x end fraction open parentheses x squared plus 1 close parentheses x sin open parentheses x close parentheses minus fraction numerator d over denominator d x end fraction open parentheses x sin open parentheses x close parentheses close parentheses open parentheses x squared plus 1 close parentheses over denominator open parentheses x sin open parentheses x close parentheses close parentheses squared end fraction$

Cari turunan $fraction numerator d over denominator d x end fraction open parentheses x squared plus 1 close parentheses$

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f plus-or-minus g close parentheses apostrophe end cell equals cell f apostrophe plus-or-minus g apostrophe end cell row cell fraction numerator d over denominator d x end fraction open parentheses x squared plus 1 close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses x squared close parentheses plus fraction numerator d over denominator d x end fraction open parentheses 1 close parentheses end cell row blank equals cell 2 x to the power of 2 minus 1 end exponent plus 0 end cell row blank equals cell 2 x to the power of 1 plus 0 end cell row blank equals cell 2 x end cell end table$

Cari turunan $fraction numerator d over denominator d x end fraction open parentheses x sin open parentheses x close parentheses close parentheses$

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

Maka,

$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 x squared plus 1 over denominator x sin open parentheses x close parentheses end fraction close parentheses end cell equals cell fraction numerator fraction numerator d over denominator d x end fraction open parentheses x squared plus 1 close parentheses x sin open parentheses x close parentheses minus fraction numerator d over denominator d x end fraction open parentheses x sin open parentheses x close parentheses close parentheses open parentheses x squared plus 1 close parentheses over denominator open parentheses x sin open parentheses x close parentheses close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x x sin open parentheses x close parentheses minus open parentheses sin open parentheses x close parentheses plus x cos open parentheses x close parentheses close parentheses open parentheses x squared plus 1 close parentheses over denominator open parentheses x sin open parentheses x close parentheses close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x to the power of 1 plus 1 end exponent sin open parentheses x close parentheses minus open parentheses sin open parentheses x close parentheses plus x cos open parentheses x close parentheses close parentheses open parentheses x squared plus 1 close parentheses over denominator open parentheses x sin open parentheses x close parentheses close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x squared sin open parentheses x close parentheses minus open parentheses sin open parentheses x close parentheses plus x cos open parentheses x close parentheses close parentheses open parentheses x squared plus 1 close parentheses over denominator open parentheses x sin open parentheses x close parentheses close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x squared sin open parentheses x close parentheses minus open parentheses sin open parentheses x close parentheses plus x cos open parentheses x close parentheses close parentheses open parentheses x squared plus 1 close parentheses over denominator x squared sin squared open parentheses x close parentheses end fraction end cell end table$

Ingatlah aturan berikut,

Maka,

Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 x squared sin open parentheses x close parentheses minus open parentheses sin open parentheses x close parentheses plus x cos open parentheses x close parentheses close parentheses open parentheses x squared plus 1 close parentheses over denominator x squared sin squared open parentheses x close parentheses end fraction end cell row blank equals cell fraction numerator 2 x squared sin open parentheses x close parentheses minus x squared sin open parentheses x close parentheses minus sin open parentheses x close parentheses minus x cubed cos open parentheses x close parentheses minus x cos open parentheses x close parentheses over denominator x squared sin squared open parentheses x close parentheses end fraction end cell row blank equals cell fraction numerator x squared sin open parentheses x close parentheses minus sin open parentheses x close parentheses minus x cubed cos open parentheses x close parentheses minus x cos open parentheses x close parentheses over denominator x squared sin squared open parentheses x close parentheses end fraction end cell end table$

Jadi, turunan dari $h left parenthesis x right parenthesis equals fraction numerator x squared plus 1 over denominator x space sin space x end fraction$ adalah $h apostrophe left parenthesis x right parenthesis equals fraction numerator x squared sin open parentheses x close parentheses minus sin open parentheses x close parentheses minus x cubed cos open parentheses x close parentheses minus x cos open parentheses x close parentheses over denominator x squared sin squared open parentheses x close parentheses end fraction$ .