Pertanyaan

Turunan pertama dari fungsi g ( x ) = ln 2 1 6 x adalah ....

Turunan pertama dari fungsi $g (x) = \frac{1 6 ^{x}}{ln 2}$ adalah ....

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Ingat bahwa turunan pertama dari adalah . Kemudian, turunan pertama dari g(x) = k⋅f(x) adalah g'(x) = k⋅f'(x). Misalkan , maka . Oleh karena itu, Jadi, jawaban yang tepat adalah B.

Ingat bahwa turunan pertama dari adalah .
Kemudian, turunan pertama dari g(x) = k⋅f(x) adalah g'(x) = k⋅f'(x).
Misalkan , maka .
Oleh karena itu,

$begin mathsize 14px style straight g left parenthesis straight x right parenthesis equals fraction numerator 16 to the power of straight x over denominator ln space 2 end fraction straight g left parenthesis straight x right parenthesis equals fraction numerator 1 over denominator ln space 2 end fraction times 16 to the power of straight x straight g left parenthesis straight x right parenthesis equals fraction numerator 1 over denominator ln space 2 end fraction times straight f left parenthesis straight x right parenthesis straight g to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator 1 over denominator ln space 2 end fraction times straight f to the power of apostrophe left parenthesis straight x right parenthesis straight g to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator 1 over denominator ln space 2 end fraction times 16 to the power of straight x space ln space 16 straight g to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator 16 to the power of straight x space ln space 16 over denominator ln space 2 end fraction straight g to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator 16 to the power of straight x space ln space 2 to the power of 4 over denominator ln space 2 end fraction straight g to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator 16 to the power of straight x times 4 space ln space 2 over denominator ln space 2 end fraction straight g to the power of apostrophe left parenthesis straight x right parenthesis equals 16 to the power of straight x times 4 straight g to the power of apostrophe left parenthesis straight x right parenthesis equals left parenthesis 4 squared right parenthesis to the power of straight x times 4 straight g to the power of apostrophe left parenthesis straight x right parenthesis equals 4 to the power of 2 straight x end exponent times 4 straight g to the power of apostrophe left parenthesis straight x right parenthesis equals 4 to the power of 2 straight x plus 1 end exponent end style$

Jadi, jawaban yang tepat adalah B.