Pertanyaan

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

Turunan pertama dari fungsi $f (x) = \frac{10 x}{5 x ^{2} - 3}$ adalah...

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

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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 :

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

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