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Turunan fungsi  adalah ...

Pertanyaan

Turunan fungsi begin mathsize 14px style y equals cube root of open parentheses 3 x to the power of 4 minus 8 close parentheses squared end root end style adalah ...

  1.  begin mathsize 14px style 8 x cubed space cube root of 3 x squared minus 8 end root end style 

  2. begin mathsize 14px style fraction numerator 24 x cubed over denominator square root of open parentheses 3 x squared minus 8 close parentheses cubed end root end fraction end style  

  3. begin mathsize 14px style fraction numerator 6 x cubed over denominator cube root of 3 x squared minus 8 end root end fraction end style  

  4.  begin mathsize 14px style fraction numerator 8 x cubed over denominator cube root of 3 x to the power of 4 minus 8 end root end fraction end style 

  5.  begin mathsize 14px style fraction numerator 8 x cubed over denominator cube root of 12 x cubed minus 8 end root end fraction end style 

Pembahasan Video:

Pembahasan Soal:

Perlu diingat rumus turunan berantai untuk bentuk fungsi aljabar, yaitu apabila begin mathsize 14px style y equals open parentheses f left parenthesis x right parenthesis close parentheses to the power of n end style maka begin mathsize 14px style y apostrophe equals n times open parentheses f left parenthesis x right parenthesis close parentheses to the power of n minus 1 end exponent times open parentheses f apostrophe left parenthesis x right parenthesis close parentheses end style.

Diketahui fungsi begin mathsize 14px style y equals cube root of open parentheses 3 x to the power of 4 minus 8 close parentheses squared end root end style atau dapat juga dituliskan sebagai begin mathsize 14px style y equals left parenthesis 3 x to the power of 4 minus 8 right parenthesis to the power of 2 over 3 end exponent end style. Turunan pertama dari fungsi tersebut adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe end cell equals cell 2 over 3 open parentheses 3 x to the power of 4 minus 8 close parentheses to the power of negative 1 third end exponent open parentheses 12 x cubed close parentheses end cell row cell y apostrophe end cell equals cell fraction numerator 24 x cubed over denominator 3 end fraction open parentheses 3 x to the power of 4 minus 8 close parentheses to the power of negative 1 third end exponent end cell row cell y apostrophe end cell equals cell fraction numerator 8 x cubed over denominator cube root of 3 x to the power of 4 minus 8 end root end fraction end cell end table end style  

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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