Turunan pertama dari adalah ….

Pertanyaan

Turunan pertama dari $begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator straight x squared plus 3 over denominator square root of straight x end fraction end style$ adalah ….

$begin mathsize 14px style fraction numerator 3 square root of straight x over denominator 2 end fraction plus fraction numerator 3 square root of straight x over denominator 2 straight x end fraction end style$
$begin mathsize 14px style fraction numerator 3 square root of straight x over denominator 2 end fraction minus fraction numerator 1 over denominator 2 square root of straight x end fraction end style$
$begin mathsize 14px style fraction numerator 3 square root of straight x over denominator 2 end fraction plus fraction numerator 1 over denominator straight x square root of straight x end fraction end style$
$begin mathsize 14px style fraction numerator 3 square root of straight x over denominator 2 end fraction minus fraction numerator 3 over denominator 2 straight x square root of straight x end fraction end style$
$begin mathsize 14px style fraction numerator straight x square root of straight x over denominator 2 end fraction minus fraction numerator 3 over denominator square root of straight x end fraction end style$

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Untuk memudahkan, gunakan aturan turunan berikut ini.

Maka,

Sederhanakan terlebih dahulu .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f open parentheses straight x close parentheses end cell equals cell fraction numerator straight x squared plus 3 over denominator square root of straight x end fraction end cell row cell straight f open parentheses straight x close parentheses end cell equals cell fraction numerator straight x squared plus 3 over denominator straight x to the power of 1 half end exponent end fraction end cell row blank equals cell straight x squared over straight x to the power of 1 half end exponent plus 3 over straight x to the power of 1 half end exponent end cell row blank equals cell straight x to the power of 2 minus 1 half end exponent plus 3 straight x to the power of negative 1 half end exponent end cell row blank equals cell straight x to the power of 3 over 2 end exponent plus 3 straight x to the power of negative 1 half end exponent end cell end table end style$

Kemudian turunkan setiap suku dari fungsi tersebut.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f to the power of straight apostrophe open parentheses straight x close parentheses end cell equals cell 3 over 2 open parentheses straight x to the power of 3 over 2 minus 1 end exponent close parentheses minus 1 half open parentheses 3 straight x to the power of negative 1 half minus 1 end exponent close parentheses end cell row blank equals cell 3 over 2 straight x to the power of 1 half end exponent minus 3 over 2 straight x to the power of negative 3 over 2 end exponent end cell row blank equals cell fraction numerator 3 square root of straight x over denominator 2 end fraction minus fraction numerator 3 over denominator 2 straight x square root of straight x end fraction end cell end table end style$

Jadi, jawaban yang benar adalah D.