Pertanyaan

7. Jika f ( x ) = x 2 cot x maka f ( 4 1 π ) = ...

7. Jika $f (x) = x^{2} cot x$ maka $f (\frac{1}{4} π) = ...$

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

jawaban yang benar adalah B. space

Pembahasan

Turunan fungsi yaitu , danaturan perkalianpada turunan yaitu: untuk menyelesaikan soal di atas, perhatikan penghitungan berikut: Oleh karena itu, jawaban yang benar adalah B.

Turunan fungsi f open parentheses x close parentheses equals cot space x yaitu f apostrophe open parentheses x close parentheses equals negative cosec squared space x , dan aturan perkalian pada turunan yaitu:

f open parentheses x close parentheses equals u v f apostrophe open parentheses x close parentheses equals u apostrophe v plus u v apostrophe

untuk menyelesaikan soal di atas, perhatikan penghitungan berikut:

$f open parentheses x close parentheses equals x squared space cot space x u equals x squared rightwards arrow u apostrophe equals 2 x v equals cot space x rightwards arrow v apostrophe equals negative cosec squared space x f apostrophe open parentheses x close parentheses equals u apostrophe v plus u v apostrophe f apostrophe open parentheses x close parentheses equals 2 x space cot space x plus x squared open parentheses negative cosec squared space x close parentheses f apostrophe open parentheses x close parentheses equals 2 x space cot space x minus x squared space cosec squared space x f apostrophe open parentheses 1 fourth straight pi close parentheses equals 2 open parentheses 1 fourth straight pi close parentheses space cot space open parentheses 1 fourth straight pi close parentheses minus open parentheses 1 fourth straight pi close parentheses squared space cosec squared space open parentheses 1 fourth straight pi close parentheses f apostrophe open parentheses 1 fourth straight pi close parentheses equals 1 half straight pi times fraction numerator 1 over denominator tan space open parentheses 1 fourth straight pi close parentheses end fraction minus 1 over 16 straight pi squared space open parentheses fraction numerator 1 over denominator sin open parentheses 1 fourth straight pi close parentheses space end fraction close parentheses squared f apostrophe open parentheses 1 fourth straight pi close parentheses equals 1 half straight pi times fraction numerator 1 over denominator tan space 45 degree end fraction minus 1 over 16 straight pi squared space open parentheses fraction numerator 1 over denominator sin space 45 degree space end fraction close parentheses squared f apostrophe open parentheses 1 fourth straight pi close parentheses equals 1 half straight pi times 1 over 1 minus 1 over 16 straight pi squared space open parentheses fraction numerator 1 over denominator begin display style 1 half end style square root of 2 space end fraction close parentheses squared f apostrophe open parentheses 1 fourth straight pi close parentheses equals 1 half straight pi times 1 over 1 minus 1 over 16 straight pi squared space open parentheses fraction numerator 2 over denominator begin display style square root of 2 space end style end fraction close parentheses squared f apostrophe open parentheses 1 fourth straight pi close parentheses equals 1 half straight pi minus fraction numerator 1 over denominator up diagonal strike 16 end fraction straight pi squared times up diagonal strike 2 f apostrophe open parentheses 1 fourth straight pi close parentheses equals 1 half straight pi minus 1 over 8 straight pi squared straight f apostrophe open parentheses 1 fourth straight pi close parentheses equals 1 half straight pi open parentheses 1 minus 1 fourth straight pi close parentheses$

Oleh karena itu, jawaban yang benar adalah B. space