Pertanyaan

Misalkan f ( x ) = sin ( sin ( sin x 2 )) , maka f ( 2 π ) adalah...

Misalkan $f (x) = sin (sin (sin x^{2}))$ , maka $f (\frac{π}{2})$ adalah...

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Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Pembahasan

Ingatlah! Maka, Cari turunan Maka, Subtitusi Kemudian cari turunan Cari turunan Maka, Di dapatkan, Kemudian cari . Maka, Jadi, hasil dari adalah . Oleh karena itu, jawaban yang benar adalah A.

Ingatlah!

$fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction equals fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row f equals cell sin open parentheses u close parentheses comma end cell row u equals cell sin open parentheses sin open parentheses x squared close parentheses close parentheses end cell row cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses sin open parentheses u close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses end cell end table$

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

$fraction numerator d over denominator d u end fraction open parentheses sin open parentheses u close parentheses close parentheses equals cos open parentheses u close parentheses$

Maka,

$fraction numerator d over denominator d u end fraction open parentheses sin open parentheses u close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses equals cos open parentheses u close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses$

Subtitusi u equals sin open parentheses sin open parentheses x squared close parentheses close parentheses

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d u end fraction open parentheses sin open parentheses u close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses end cell equals cell cos open parentheses u close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses end cell row blank equals cell cos open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses end cell end table end style$

Kemudian cari turunan $fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction end cell equals cell fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses sin open parentheses u close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x squared close parentheses close parentheses end cell row blank equals cell cos open parentheses u close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x squared close parentheses close parentheses end cell row cell subtitusi space u end cell equals cell sin open parentheses x squared close parentheses end cell row cell cos open parentheses u close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x squared close parentheses close parentheses end cell equals cell cos open parentheses sin open parentheses x squared close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x squared close parentheses close parentheses end cell end table$

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

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction end cell equals cell fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row f equals cell sin left parenthesis u right parenthesis end cell row u equals cell x squared end cell row cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x squared close parentheses close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses sin open parentheses u close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses x squared close parentheses end cell row blank equals cell cos open parentheses u close parentheses fraction numerator d over denominator d x end fraction open parentheses x squared close parentheses end cell row blank equals cell cos open parentheses x squared close parentheses fraction numerator d over denominator d x end fraction open parentheses x squared close parentheses end cell row blank equals cell cos open parentheses x squared close parentheses times 2 x to the power of 2 minus 1 end exponent end cell row blank equals cell cos open parentheses x squared close parentheses times thin space 2 x end cell row blank blank blank end table$

Maka, $table attributes columnalign right center left columnspacing 0px end attributes row cell cos open parentheses u close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x squared close parentheses close parentheses end cell equals cell cos open parentheses sin open parentheses x squared close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses x squared close parentheses close parentheses end cell row blank equals cell cos open parentheses sin open parentheses x squared close parentheses close parentheses cos open parentheses x squared close parentheses times thin space 2 x end cell end table$

Di dapatkan,

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses sin open parentheses u close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell cos open parentheses sin open parentheses sin open parentheses x squared close parentheses close parentheses close parentheses cos open parentheses sin open parentheses x squared close parentheses close parentheses cos open parentheses x squared close parentheses times thin space 2 x end cell end table end style$

Kemudian cari f apostrophe open parentheses square root of straight pi over 2 end root close parentheses .

table attributes columnalign right center left columnspacing 0px end attributes row cell sin 90 end cell equals 1 row cell cos 90 end cell equals 0 end table

Maka,

Jadi, hasil dari f apostrophe open parentheses square root of straight pi over 2 end root close parentheses adalah .

Oleh karena itu, jawaban yang benar adalah A.