Pertanyaan

Turunan pertama dari fungsi f ( x ) = ( 3 1 ) x adalah ....

Turunan pertama dari fungsi $f (x) = (\frac{1}{3})^{x}$ adalah ....

$begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator ln space 3 over denominator 3 to the power of straight x end fraction end style$
$begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals negative fraction numerator ln space 3 over denominator 3 to the power of straight x end fraction end style$
$begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator 1 over denominator 3 to the power of straight x space ln space 3 end fraction end style$
$begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals negative fraction numerator 1 over denominator 3 to the power of straight x space ln space 3 end fraction end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Ingat bahwa turunan pertama dari adalah . Perhatikan bahwa Misalkan u(x) = - x, maka didapat u'(x) = - 1. Oleh karena itu, Jadi, jawaban yang tepat adalah B.

Ingat bahwa turunan pertama dari adalah .
Perhatikan bahwa

Misalkan u(x) = - x, maka didapat u'(x) = - 1.

Oleh karena itu,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis end cell equals cell 3 to the power of negative straight x end exponent end cell row cell straight f left parenthesis straight x right parenthesis end cell equals cell 3 to the power of straight u left parenthesis straight x right parenthesis end exponent end cell row cell straight f to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell 3 to the power of straight u left parenthesis straight x right parenthesis end exponent space ln space 3 times straight u to the power of apostrophe left parenthesis straight x right parenthesis end cell row cell straight f to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell 3 to the power of negative straight x end exponent space ln space 3 times left parenthesis negative 1 right parenthesis end cell row cell straight f to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell negative 3 to the power of negative straight x end exponent space ln space 3 end cell row cell straight f to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell negative 1 over 3 to the power of straight x ln space 3 end cell row cell straight f to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell negative fraction numerator ln space 3 over denominator 3 to the power of straight x end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah B.