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Pertanyaan

Turunan pertama dari begin mathsize 14px style straight f open parentheses straight x close parentheses equals open parentheses 4 straight x squared plus 3 close parentheses to the power of 5 open parentheses 2 straight x minus 3 close parentheses to the power of 4 end style adalah ….

  1. undefined 

  2. begin mathsize 14px style 8 open parentheses 4 x squared plus 3 close parentheses to the power of 4 open parentheses 2 x minus 3 close parentheses cubed open parentheses 12 x squared plus 14 x minus 3 close parentheses end style 

  3. begin mathsize 14px style 8 open parentheses 4 x squared plus 3 close parentheses to the power of 4 open parentheses 2 x minus 3 close parentheses cubed open parentheses 15 x squared minus 12 x plus 6 close parentheses end style 

  4. begin mathsize 14px style 12 open parentheses 4 straight x squared plus 3 close parentheses to the power of 4 open parentheses 2 straight x minus 3 close parentheses cubed open parentheses 4 straight x squared minus 10 straight x plus 2 close parentheses end style

  5. begin mathsize 14px style 12 open parentheses 4 straight x squared plus 3 close parentheses to the power of 4 open parentheses 2 straight x minus 3 close parentheses cubed open parentheses 3 straight x squared minus 10 straight x plus 2 close parentheses end style

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Misalkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight u open parentheses straight x close parentheses end cell equals cell open parentheses 4 straight x squared plus 3 close parentheses to the power of 5 end cell row cell straight v open parentheses straight x close parentheses end cell equals cell open parentheses 2 straight x minus 3 close parentheses to the power of 4 end cell end table end style

Maka diperoleh turunan dari masing-masing fungsi tersebut yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight u to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell 5 times left parenthesis 4 straight x squared plus 3 right parenthesis to the power of left parenthesis 5 minus 1 right parenthesis times left parenthesis 8 straight x plus 0 right parenthesis end cell row blank equals cell 40 straight x left parenthesis 4 straight x squared plus 3 right parenthesis to the power of 4 end cell row cell straight v to the power of straight apostrophe open parentheses straight x close parentheses end cell equals cell 4 times open parentheses 2 straight x minus 3 close parentheses to the power of 4 minus 1 end exponent times open parentheses 2 minus 0 close parentheses end cell row blank equals cell 8 open parentheses 2 straight x minus 3 close parentheses cubed end cell end table end style

Dengan menggunakan aturan perkalian pada turunan maka diperoleh,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis end cell equals cell straight u left parenthesis straight x right parenthesis times straight v left parenthesis straight x right parenthesis end cell row cell straight f to the power of straight apostrophe left parenthesis straight x right parenthesis end cell equals cell straight u to the power of straight apostrophe left parenthesis straight x right parenthesis times straight v left parenthesis straight x right parenthesis plus straight u left parenthesis straight x right parenthesis times straight v to the power of straight apostrophe left parenthesis straight x right parenthesis end cell row blank equals cell 40 straight x left parenthesis 4 straight x squared plus 3 right parenthesis to the power of 4 times left parenthesis 2 straight x minus 3 right parenthesis to the power of 4 plus left parenthesis 4 straight x squared plus 3 right parenthesis to the power of 5 times 8 left parenthesis 2 straight x minus 3 right parenthesis cubed end cell row blank equals cell left parenthesis 4 straight x squared plus 3 right parenthesis to the power of 4 left parenthesis 2 straight x minus 3 right parenthesis cubed left square bracket 40 straight x left parenthesis 2 straight x minus 3 right parenthesis plus left parenthesis 4 straight x squared plus 3 right parenthesis 8 right square bracket end cell row blank equals cell left parenthesis 4 straight x squared plus 3 right parenthesis to the power of 4 left parenthesis 2 straight x minus 3 right parenthesis cubed left square bracket 80 straight x squared minus 120 straight x plus 32 straight x squared plus 24 right square bracket space end cell row blank equals cell left parenthesis 4 straight x squared plus 3 right parenthesis to the power of 4 left parenthesis 2 straight x minus 3 right parenthesis cubed left parenthesis 112 straight x squared minus 120 straight x plus 24 right parenthesis space end cell row blank equals cell 8 left parenthesis 4 straight x squared plus 3 right parenthesis to the power of 4 left parenthesis 2 straight x minus 3 right parenthesis cubed left parenthesis 14 straight x squared minus 15 straight x plus 3 right parenthesis end cell end table end style  

 

Jadi, jawaban yang tepat adalah A.

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