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Turunan pertama dari fungsi f ( x ) = 5 x 2 − 3 ​ 10 x ​ adalah...

Turunan pertama dari fungsi adalah...

  1. fraction numerator 25 x minus 30 over denominator open parentheses 5 x squared minus 3 close parentheses square root of 5 x squared minus 3 end root end fraction

  2. fraction numerator 30 x squared plus 25 over denominator open parentheses 5 x squared minus 3 close parentheses square root of 5 x squared minus 3 end root end fraction

  3. fraction numerator 30 x squared minus 25 over denominator open parentheses 5 x squared minus 3 close parentheses square root of 5 x squared minus 3 end root end fraction

  4. fraction numerator 25 x squared plus 30 over denominator open parentheses 5 x squared minus 3 close parentheses square root of 5 x squared minus 3 end root end fraction

  5. fraction numerator 25 x squared minus 30 over denominator open parentheses 5 x squared minus 3 close parentheses square root of 5 x squared minus 3 end root end fraction

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N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

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Pembahasan

Misal :

  • f left parenthesis x right parenthesis equals fraction numerator 10 x over denominator square root of 5 x squared minus 3 end root end fraction

Misal :

U equals 10 x  U apostrophe equals 10  V equals square root of 5 x squared minus 3 end root equals open parentheses 5 x squared minus 3 close parentheses to the power of 1 half end exponent  V apostrophe equals 1 half open parentheses 5 x squared minus 3 close parentheses to the power of negative 1 half end exponent.10 x  equals fraction numerator 5 x over denominator square root of 5 x squared minus 3 end root end fraction

  • y equals U over V rightwards arrow y apostrophe equals fraction numerator U apostrophe V minus U V apostrophe over denominator V squared end fraction  f apostrophe left parenthesis x right parenthesis equals fraction numerator 10 square root of 5 x squared minus 3 end root minus begin display style fraction numerator 5 over denominator square root of 5 x squared minus 3 end root end fraction end style.10 x over denominator open parentheses square root of 5 x squared minus 3 end root close parentheses squared end fraction  equals fraction numerator 10 left parenthesis 5 x squared space minus space 3 right parenthesis minus space 25 x squared over denominator left parenthesis 5 x squared minus space 3 right parenthesis. square root of 5 x squared space minus space 3 end root end fraction  equals fraction numerator 25 x squared space minus 30 over denominator open parentheses 5 x squared minus 3 close parentheses square root of 5 x squared minus 3 end root end fraction

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