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Dengan menggunakan aturan rantai tentukan turunan dari fungsi berikut ! f ( x ) = 3 x − 2 2 x + 6

Dengan menggunakan aturan rantai tentukan turunan dari fungsi berikut !

$f (x) = \frac{2 x + 6}{3 x - 2}$

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Aturan rantai dapat dibuat,

Aturan rantai dapat dibuat, left parenthesis f o g right parenthesis apostrophe left parenthesis x right parenthesis space equals space f apostrophe left parenthesis g left parenthesis x right parenthesis right parenthesis space. space g apostrophe left parenthesis x right parenthesis

$u space equals space 2 x plus 6 u apostrophe space equals space 2 v space equals space open parentheses 3 x minus 2 close parentheses to the power of 1 half end exponent v apostrophe space equals space 1 half open parentheses 3 x minus 2 close parentheses to the power of negative 1 half end exponent space. space 3 v apostrophe space equals space fraction numerator 3 over denominator 2 square root of 3 x minus 2 end root end fraction f apostrophe left parenthesis x right parenthesis space equals space fraction numerator u apostrophe v space minus space v apostrophe u over denominator v squared end fraction f apostrophe left parenthesis x right parenthesis space equals space fraction numerator open parentheses 2 close parentheses open parentheses square root of 3 x minus 2 end root close parentheses space minus space open parentheses fraction numerator 3 over denominator 2 square root of 3 x minus 2 end root end fraction close parentheses open parentheses 2 x plus 6 close parentheses over denominator open parentheses open parentheses 3 x minus 2 close parentheses to the power of 1 half end exponent close parentheses squared end fraction f apostrophe left parenthesis x right parenthesis space equals space fraction numerator 2 square root of 3 x minus 2 end root minus space open parentheses fraction numerator 3 over denominator 2 square root of 3 x minus 2 end root end fraction close parentheses open parentheses 2 x plus 6 close parentheses over denominator 3 x minus 2 end fraction$