Pertanyaan

Turunan pertama dari f ( x ) = 5 x + 2 x 2 − 3 adalah f ( x ) . Nilai f ( 0 ) = ....

$Turunan pertama dari f (x) = \frac{x ^{2} - 3}{5 x + 2} adalah f (x) . Nilai f (0) = ....$

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

$Fungsi space straight f left parenthesis straight x right parenthesis equals straight u over straight v memiliki space fungsi space turunan space straight f apostrophe left parenthesis straight x right parenthesis space fraction numerator straight u apostrophe. straight v minus straight u. straight v apostrophe over denominator straight v squared end fraction sehingga straight u equals straight x squared minus 3 space rightwards arrow straight u apostrophe equals 2 straight x straight v equals 5 straight x plus 2 space rightwards arrow straight v apostrophe equals 5 straight f left parenthesis straight x right parenthesis equals fraction numerator straight x squared minus 3 over denominator 5 straight x plus 2 end fraction straight f apostrophe left parenthesis straight x right parenthesis equals fraction numerator 2 straight x left parenthesis 5 straight x plus 2 right parenthesis minus left parenthesis straight x squared minus 3 right parenthesis 5 over denominator left parenthesis 5 straight x plus 2 right parenthesis squared end fraction straight f apostrophe left parenthesis straight x right parenthesis equals fraction numerator left parenthesis 10 straight x squared plus 4 straight x right parenthesis minus left parenthesis 5 straight x squared minus 15 right parenthesis over denominator left parenthesis 5 straight x plus 2 right parenthesis squared end fraction straight f apostrophe left parenthesis straight x right parenthesis equals fraction numerator 5 straight x squared plus 4 straight x plus 15 over denominator left parenthesis 5 straight x plus 2 right parenthesis squared end fraction Untuk space straight x equals 0 comma space didapat straight f apostrophe left parenthesis 0 right parenthesis equals fraction numerator 5 left parenthesis 0 right parenthesis squared plus 4 left parenthesis 0 right parenthesis plus 15 over denominator left parenthesis 5 left parenthesis 0 right parenthesis plus 2 right parenthesis squared end fraction straight f apostrophe left parenthesis 0 right parenthesis equals 15 over 4$