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Diketahui  dan  adalah turunan pertama . Nilai  adalah ...

Pertanyaan

Diketahui straight f left parenthesis straight x right parenthesis equals cube root of open parentheses 2 straight x cubed plus 3 straight x plus 3 close parentheses squared end root dan straight f apostrophe left parenthesis straight x right parenthesis adalah turunan pertama straight f left parenthesis straight x right parenthesis. Nilai straight f apostrophe left parenthesis 1 right parenthesis adalah ...

  1. 1 

  2. 2 

  3. 3 

  4. negative 3 

  5. negative 1 

Pembahasan Soal:

Diketahui straight f left parenthesis straight x right parenthesis equals cube root of open parentheses 2 straight x cubed plus 3 straight x plus 3 close parentheses squared end root. Turunan pertama dari f left parenthesis x right parenthesis adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis end cell equals cell cube root of open parentheses 2 straight x cubed plus 3 straight x plus 3 close parentheses squared end root end cell row cell straight f left parenthesis straight x right parenthesis end cell equals cell open parentheses 2 straight x cubed plus 3 straight x plus 3 close parentheses to the power of 2 over 3 end exponent end cell row cell straight f apostrophe left parenthesis straight x right parenthesis end cell equals cell 2 over 3 open parentheses 2 straight x cubed plus 3 straight x plus 3 close parentheses to the power of 2 over 3 minus 1 end exponent open parentheses 6 straight x squared plus 3 close parentheses end cell row cell straight f apostrophe left parenthesis straight x right parenthesis end cell equals cell 2 over 3 open parentheses 2 straight x cubed plus 3 straight x plus 3 close parentheses to the power of negative 1 third end exponent open parentheses 6 straight x squared plus 3 close parentheses end cell row cell straight f apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator 2 open parentheses 6 straight x squared plus 3 close parentheses over denominator 3 cube root of 2 straight x cubed plus 3 straight x plus 3 end root end fraction end cell row cell straight f apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator 12 straight x squared plus 6 over denominator 3 cube root of 2 straight x cubed plus 3 straight x plus 3 end root end fraction end cell end table 

Nilai dari straight f apostrophe left parenthesis 1 right parenthesis adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f apostrophe left parenthesis 1 right parenthesis end cell equals cell fraction numerator 12 left parenthesis 1 right parenthesis squared plus 6 over denominator 3 cube root of 2 left parenthesis 1 right parenthesis cubed plus 3 left parenthesis 1 right parenthesis plus 3 end root end fraction end cell row blank equals cell fraction numerator 12 plus 6 over denominator 3 cube root of 2 plus 3 plus 3 end root end fraction end cell row blank equals cell fraction numerator 18 over denominator 3 cube root of 8 end fraction end cell row blank equals cell fraction numerator 18 over denominator 3 open parentheses 2 close parentheses end fraction end cell row blank equals cell 18 over 6 end cell row blank equals 3 end table 

Jadi, nilai straight f apostrophe left parenthesis 1 right parenthesis adalah 3.

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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