Pertanyaan

Tentukan turunan dari fungsi-fungsi trigonometri berikut. e. g ( x ) = sin x + cos x cos x − sin x

Tentukan turunan dari fungsi-fungsi trigonometri berikut.

e. $g (x) = \frac{cos x - sin x}{sin x + cos x}$

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Habis dalam

Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

turunan dari adalah .

turunan dari $g left parenthesis x right parenthesis equals fraction numerator cos space x minus sin space x over denominator sin space x space plus space cos space x end fraction$ adalah $g apostrophe left parenthesis x right parenthesis equals negative fraction numerator 2 over denominator 1 plus sin open parentheses 2 x close parentheses end fraction$ .

Pembahasan

Ingatlah! Maka, Cari turunan . Cari turunan Maka, Menyederhanakan, Maka, Menyederhanakan, Maka, Menyederhanakan, Maka, Karena, Maka, Maka, Jadi, turunan dari adalah .

Ingatlah!

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

Maka,

$begin mathsize 12px style fraction numerator d over denominator d x end fraction open parentheses fraction numerator cos open parentheses x close parentheses minus sin open parentheses x close parentheses over denominator sin open parentheses x close parentheses plus cos open parentheses x close parentheses end fraction close parentheses equals fraction numerator fraction numerator d over denominator d x end fraction open parentheses cos open parentheses x close parentheses minus sin open parentheses x close parentheses close parentheses open parentheses sin open parentheses x close parentheses plus cos open parentheses x close parentheses close parentheses minus fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x close parentheses plus cos open parentheses x close parentheses close parentheses open parentheses cos open parentheses x close parentheses minus sin open parentheses x close parentheses close parentheses over denominator open parentheses sin open parentheses x close parentheses plus cos open parentheses x close parentheses close parentheses squared end fraction end style$

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

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

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

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

Maka,

Menyederhanakan,

Maka,

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

Menyederhanakan,

Maka,

Menyederhanakan,

Maka,

$begin mathsize 12px style 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 cos open parentheses x close parentheses minus sin open parentheses x close parentheses over denominator sin open parentheses x close parentheses plus cos open parentheses x close parentheses end fraction close parentheses end cell equals cell fraction numerator open parentheses negative sin open parentheses x close parentheses minus cos open parentheses x close parentheses close parentheses open parentheses sin open parentheses x close parentheses plus cos open parentheses x close parentheses close parentheses minus open parentheses cos open parentheses x close parentheses minus sin open parentheses x close parentheses close parentheses squared over denominator 1 plus sin open parentheses 2 x close parentheses end fraction end cell row blank equals cell fraction numerator negative open parentheses cos squared open parentheses x close parentheses minus 2 cos open parentheses x close parentheses sin open parentheses x close parentheses plus sin squared open parentheses x close parentheses close parentheses plus open parentheses negative cos open parentheses x close parentheses minus sin open parentheses x close parentheses close parentheses open parentheses cos open parentheses x close parentheses plus sin open parentheses x close parentheses close parentheses over denominator 1 plus sin open parentheses 2 x close parentheses end fraction end cell row blank equals cell fraction numerator negative cos squared open parentheses x close parentheses plus up diagonal strike 2 cos open parentheses x close parentheses sin open parentheses x close parentheses end strike minus sin squared open parentheses x close parentheses minus cos squared open parentheses x close parentheses minus up diagonal strike 2 sin open parentheses x close parentheses cos open parentheses x close parentheses end strike minus sin squared open parentheses x close parentheses over denominator 1 plus sin left parenthesis 2 x right parenthesis end fraction end cell row blank equals cell fraction numerator negative cos squared open parentheses x close parentheses minus sin squared open parentheses x close parentheses minus cos squared open parentheses x close parentheses minus sin squared open parentheses x close parentheses over denominator 1 plus sin left parenthesis 2 x right parenthesis end fraction end cell row blank equals cell fraction numerator negative cos squared left parenthesis x right parenthesis minus cos squared left parenthesis x right parenthesis minus sin squared left parenthesis x right parenthesis minus sin squared left parenthesis x right parenthesis over denominator 1 plus sin left parenthesis 2 x right parenthesis end fraction end cell row blank equals cell fraction numerator negative 2 cos squared open parentheses x close parentheses minus sin squared open parentheses x close parentheses minus sin squared open parentheses x close parentheses over denominator 1 plus sin left parenthesis 2 x right parenthesis end fraction end cell row blank equals cell fraction numerator negative 2 cos squared open parentheses x close parentheses minus 2 sin squared open parentheses x close parentheses over denominator 1 plus sin left parenthesis 2 x right parenthesis end fraction end cell end table end style$

Karena,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos squared left parenthesis x right parenthesis plus sin squared left parenthesis x right parenthesis end cell equals 1 row cell cos squared left parenthesis x right parenthesis end cell equals cell 1 minus sin squared open parentheses x close parentheses end cell end table

Maka,

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

Jadi, turunan dari $g left parenthesis x right parenthesis equals fraction numerator cos space x minus sin space x over denominator sin space x space plus space cos space x end fraction$ adalah $g apostrophe left parenthesis x right parenthesis equals negative fraction numerator 2 over denominator 1 plus sin open parentheses 2 x close parentheses end fraction$ .