Roboguru

Diketahui .

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals open parentheses x cubed minus x squared plus 1 close parentheses cubed open parentheses 3 x squared minus 2 x close parentheses end stylebegin mathsize 14px style f apostrophe open parentheses 0 close parentheses plus f apostrophe open parentheses 1 close parentheses equals space horizontal ellipsis end style 

  1. begin mathsize 14px style 8 end style 

  2. begin mathsize 14px style 5 end style 

  3. begin mathsize 14px style 3 end style 

  4. begin mathsize 14px style negative 6 end style 

  5. begin mathsize 14px style negative 7 end style 

Jawaban:

Aturan turunan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell u open parentheses x close parentheses times v open parentheses x close parentheses space rightwards arrow space f apostrophe open parentheses x close parentheses equals u apostrophe open parentheses x close parentheses times v open parentheses x close parentheses plus u open parentheses x close parentheses times v apostrophe open parentheses x close parentheses end cell row cell f open parentheses x close parentheses end cell equals cell open square brackets u open parentheses x close parentheses close square brackets to the power of n space rightwards arrow space f apostrophe open parentheses x close parentheses equals n times open square brackets u open parentheses x close parentheses close square brackets to the power of n minus 1 end exponent times u apostrophe open parentheses x close parentheses end cell end table end style

Turunan dari fungsi tersebut adalah sebagai berikut.

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begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses 0 close parentheses end cell equals cell 3 open parentheses 0 cubed minus 0 squared plus 1 close parentheses squared open parentheses 3 times 0 squared minus 2 times 0 close parentheses squared end cell row blank blank cell plus open parentheses 0 cubed minus 0 squared plus 1 close parentheses blank cubed open parentheses 6 times 0 minus 2 close parentheses end cell row blank equals cell 3 times 1 times 0 plus 1 times open parentheses negative 2 close parentheses end cell row blank equals cell negative 2 end cell row cell f apostrophe left parenthesis 1 right parenthesis end cell equals cell 3 left parenthesis 1 cubed minus 1 squared plus 1 right parenthesis squared left parenthesis 3 times 1 squared minus 2 times 1 right parenthesis squared end cell row blank blank cell plus left parenthesis 1 cubed minus 1 squared plus 1 right parenthesis cubed open parentheses 6 times 1 minus 2 close parentheses space end cell row blank equals cell 3 times 1 times 1 plus 1 times 4 end cell row blank equals 7 end table end style

begin mathsize 14px style f apostrophe open parentheses 0 close parentheses plus f apostrophe open parentheses 1 close parentheses equals negative 2 plus 7 equals 5 end style

Oleh karena itu, jawaban yang tepat adalah B.

 

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