Pertanyaan

Jika d x df = x sin x dan u ( x ) = co t x , maka tentukan d u df .

Jika $\frac{df}{d x} = \frac{sin x}{x}$ dan $u (x) = co t x$ , maka tentukan $\frac{df}{d u}$ .

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

adalah .

$fraction numerator d f over denominator d u end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin x over denominator x plus x cubed end fraction end cell end table$ .

Pembahasan

Karena ,cari inversnya Dengan menggunakan aturan rantai, di dapatkan Jadi, adalah .

Karena u left parenthesis x right parenthesis equals c o t space x ,cari inversnya

$table attributes columnalign right center left columnspacing 0px end attributes row cell u left parenthesis x right parenthesis end cell equals cell c o t space x end cell row cell c o t space x end cell equals cell a r c space c o t space u end cell row cell fraction numerator d x over denominator d u end fraction end cell equals cell fraction numerator 1 over denominator 1 plus x squared end fraction end cell end table$

Dengan menggunakan aturan rantai, di dapatkan

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f over denominator d u end fraction end cell equals cell fraction numerator d f over denominator d x end fraction times fraction numerator d x over denominator d u end fraction end cell row blank equals cell fraction numerator sin space x over denominator x end fraction times open parentheses negative fraction numerator 1 over denominator 1 plus x squared end fraction close parentheses end cell row blank equals cell negative fraction numerator sin x over denominator x plus x cubed end fraction end cell end table$

Jadi, $fraction numerator d f over denominator d u end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin x over denominator x plus x cubed end fraction end cell end table$ .