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Gradien garis singgung kurva f ( x ) = sin x csc x pada titik berabsis 3 2 π adalah...

Gradien garis singgung kurva $f (x) = \frac{csc x}{sin x}$ pada titik berabsis $\frac{2 π}{3}$ adalah...

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Habis dalam

Klaim

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

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Misalkan:

Maka,

$f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction f apostrophe open parentheses x close parentheses equals fraction numerator open parentheses negative c s c space x space c o t space x close parentheses open parentheses sin space x close parentheses minus c s c space x space cos space x over denominator sin squared space x end fraction f apostrophe open parentheses x close parentheses equals fraction numerator open parentheses negative begin display style fraction numerator c o t space x over denominator sin space x end fraction end style close parentheses open parentheses sin space x close parentheses minus begin display style fraction numerator 1 over denominator sin space x end fraction end style times cos space x over denominator sin squared space x end fraction f apostrophe open parentheses x close parentheses equals fraction numerator negative c o t space x minus c o t space x over denominator sin squared space x end fraction f apostrophe open parentheses x close parentheses equals fraction numerator negative 2 space c o t space x over denominator sin squared space x end fraction m equals f apostrophe open parentheses fraction numerator 2 straight pi over denominator 3 end fraction close parentheses equals fraction numerator negative 2 space c o t open parentheses begin display style fraction numerator 2 straight pi over denominator 3 end fraction end style close parentheses over denominator sin squared open parentheses fraction numerator 2 straight pi over denominator 3 end fraction close parentheses end fraction m equals fraction numerator negative 2 open parentheses negative square root of 3 close parentheses over denominator open parentheses begin display style fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses squared end fraction m equals fraction numerator 2 square root of 3 over denominator begin display style 3 over 4 end style end fraction m equals fraction numerator 8 square root of 3 over denominator 3 end fraction$

Tidak ada opsi jawaban.