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 ….

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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.

begin mathsize 14px style straight f open parentheses straight x close parentheses equals straight k open parentheses straight x close parentheses plus straight g open parentheses straight x close parentheses end style 

Maka,

begin mathsize 14px style straight f to the power of straight apostrophe open parentheses straight x close parentheses equals straight k to the power of straight apostrophe open parentheses straight x close parentheses plus straight g to the power of straight apostrophe open parentheses straight x close parentheses end style 

Sederhanakan terlebih dahulu undefined.

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.

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