Pertanyaan

turunan pertama y = sec x 1 − tan x , adalah...

turunan pertama $y = \frac{1 - tan x}{sec x}$ , adalah ...

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus tan space x over denominator sec squared space x end fraction end cell end table$
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 plus tan space x over denominator sec squared space x end fraction end cell end table$
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative fraction numerator 1 plus tan space x over denominator sec space x end fraction end cell end table$
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 plus tan space x over denominator sec space x end fraction end cell end table$
$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator tan space x minus 1 over denominator sec space x end fraction end cell end table$

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Mahasiswa/Alumni Universitas Nasional

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat aturan pembagian turunan : Diketahui : Misalkan , maka Misalkan , maka Sehingga turunan pertamanya : Maka, turunan pertamanya adalah . Oleh karena itu, jawaban yang benar adalah C.

Ingat aturan pembagian turunan :

Diketahui $y equals fraction numerator 1 minus tan space x over denominator sec space x end fraction$ :

Misalkan u equals 1 minus tan space x , maka u apostrophe equals negative sec squared space x

Misalkan v equals sec space x , maka v apostrophe equals sec space x space tan space x

Sehingga turunan pertamanya :

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator negative sec squared space x times sec space x minus sec space x times tan space x times open parentheses 1 minus tan space x close parentheses over denominator sec squared space x end fraction end cell row blank equals cell fraction numerator negative sec cubed space x minus sec space x times tan space x plus sec space x times tan squared space x over denominator sec squared space x end fraction end cell row blank equals cell fraction numerator sec space x open parentheses negative sec squared space x minus tan space x plus tan squared space x close parentheses over denominator sec squared space x end fraction end cell row blank equals cell fraction numerator negative open parentheses tan squared space x plus 1 close parentheses minus tan space x plus tan squared space x over denominator sec space x end fraction end cell row blank equals cell fraction numerator negative tan squared space x minus 1 minus tan space x plus tan squared space x over denominator sec space x end fraction end cell row blank equals cell fraction numerator negative tan squared space x plus tan squared space x minus 1 minus tan space x over denominator sec space x end fraction end cell row blank equals cell fraction numerator negative 1 minus tan space x over denominator sec space x end fraction end cell row blank equals cell negative fraction numerator 1 plus tan space x over denominator sec space x end fraction end cell end table$

Maka, turunan pertamanya adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative fraction numerator 1 plus tan space x over denominator sec space x end fraction end cell end table$ .

Oleh karena itu, jawaban yang benar adalah C.