Pertanyaan

Jika f ( x ) = 5 x e x , maka nilai dari f'(2) adalah ....

Jika $f (x) = \frac{e ^{x}}{5 x}$ , maka nilai dari f'(2) adalah ....

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat bahwa turunan pertama dari adalah Misalkan dan v(x) = 5x, maka didapat dan v'(x) = 5. Oleh karena itu, Oleh karena itu, didapat Jadi, jawaban yang tepat adalah C.

Ingat bahwa turunan pertama dari $begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals fraction numerator straight u left parenthesis straight x right parenthesis over denominator straight v left parenthesis straight x right parenthesis space end fraction end style$ adalah

$begin mathsize 14px style straight f to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator straight u to the power of apostrophe left parenthesis straight x right parenthesis straight v left parenthesis straight x right parenthesis minus straight u left parenthesis straight x right parenthesis straight v to the power of apostrophe left parenthesis straight x right parenthesis over denominator open parentheses straight v left parenthesis straight x right parenthesis close parentheses squared end fraction end style$

Misalkan dan v(x) = 5x, maka didapat dan v'(x) = 5.
Oleh karena itu,

$begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals fraction numerator straight e to the power of straight x over denominator 5 straight x end fraction straight f left parenthesis straight x right parenthesis equals fraction numerator straight u left parenthesis straight x right parenthesis over denominator straight v left parenthesis straight x right parenthesis end fraction straight f to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator straight u to the power of apostrophe left parenthesis straight x right parenthesis straight v left parenthesis straight x right parenthesis minus straight u left parenthesis straight x right parenthesis straight v to the power of apostrophe left parenthesis straight x right parenthesis over denominator left parenthesis straight v left parenthesis straight x right parenthesis right parenthesis squared end fraction straight f to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator straight e to the power of straight x times 5 straight x minus straight e to the power of straight x times 5 over denominator left parenthesis 5 straight x right parenthesis squared end fraction straight f to the power of apostrophe left parenthesis straight x right parenthesis equals fraction numerator straight e to the power of straight x left parenthesis 5 straight x minus 5 right parenthesis over denominator left parenthesis 5 straight x right parenthesis squared end fraction end style$

Oleh karena itu, didapat

$begin mathsize 14px style straight f to the power of apostrophe left parenthesis 2 right parenthesis equals fraction numerator straight e squared left parenthesis 5 times 2 minus 5 right parenthesis over denominator left parenthesis 5 times 2 right parenthesis squared end fraction straight f to the power of apostrophe left parenthesis 2 right parenthesis equals fraction numerator straight e squared left parenthesis 10 minus 5 right parenthesis over denominator left parenthesis 10 right parenthesis squared end fraction straight f to the power of apostrophe left parenthesis 2 right parenthesis equals fraction numerator straight e squared left parenthesis 5 right parenthesis over denominator 100 end fraction straight f to the power of apostrophe left parenthesis 2 right parenthesis equals straight e squared over 20 end style$

Jadi, jawaban yang tepat adalah C.