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Turunan pertama dari fungsi f ( x ) = e x 3 − x adalah ....

Turunan pertama dari fungsi adalah ....

  1. begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals straight x squared times straight e to the power of straight x cubed minus straight x end exponent end style  

  2. begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals 3 straight x squared times straight e to the power of straight x cubed minus straight x end exponent end style  

  3. begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals left parenthesis straight x squared minus 1 right parenthesis times straight e to the power of straight x cubed minus straight x end exponent end style   

  4. begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals left parenthesis 3 straight x squared minus 1 right parenthesis times straight e to the power of straight x cubed minus straight x end exponent end style  

  5. begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals left parenthesis 3 straight x squared minus 3 right parenthesis times straight e to the power of straight x cubed minus straight x end exponent end style  

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S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

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Pembahasan

Ingat bahwa turunan pertama dari adalah . Misalkan , maka didapat . Perhatikan bahwa Jadi, jawaban yang tepat adalah D.

Ingat bahwa turunan pertama dari begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals straight e to the power of straight u left parenthesis straight x right parenthesis end exponent end style adalah begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals straight e to the power of straight u left parenthesis straight x right parenthesis end exponent times straight u to the power of apostrophe left parenthesis straight x right parenthesis end style.
Misalkan begin mathsize 14px style straight u left parenthesis straight x right parenthesis equals straight x cubed minus straight x end style, maka didapat begin mathsize 14px style straight u to the power of apostrophe left parenthesis straight x right parenthesis equals 3 straight x squared minus 1 end style.
Perhatikan bahwa

begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals straight e to the power of straight x cubed minus straight x end exponent straight f left parenthesis straight x right parenthesis equals straight e to the power of straight u left parenthesis straight x right parenthesis end exponent straight f left parenthesis straight x right parenthesis equals straight e to the power of straight u left parenthesis straight x right parenthesis end exponent times straight u to the power of apostrophe left parenthesis straight x right parenthesis straight f left parenthesis straight x right parenthesis equals straight e to the power of straight x cubed minus straight x end exponent times left parenthesis 3 straight x squared minus 1 right parenthesis straight f left parenthesis straight x right parenthesis equals left parenthesis 3 straight x squared minus 1 right parenthesis times straight e to the power of straight x cubed minus straight x end exponent end style   

Jadi, jawaban yang tepat adalah D. 

 

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