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Tentukan turunan pertama dari fungsi berikut. a.

Tentukan turunan pertama undefined dari fungsi berikut.

a. begin mathsize 14px style y equals 1 over open parentheses 3 x squared plus x minus 1 close parentheses squared end style 

Jawaban:

Gunakan konsep aturan rantai sebagai berikut:

begin mathsize 14px style fraction numerator straight d y over denominator straight d x end fraction equals fraction numerator straight d y over denominator straight d u end fraction cross times fraction numerator straight d u over denominator straight d x end fraction end style 

Diketahui:

begin mathsize 14px style y equals 1 over open parentheses 3 x squared plus x minus 1 close parentheses squared end style

Misalkan begin mathsize 14px style u equals 3 x squared plus x minus 1 end style.

begin mathsize 14px style y equals 1 over u squared equals u to the power of negative 2 end exponent end style 

Akan ditentukan turunan pertama undefined dengan menggunakan aturan rantai, perhatikan perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell fraction numerator straight d y over denominator straight d x end fraction end cell equals cell fraction numerator straight d y over denominator straight d u end fraction cross times fraction numerator straight d u over denominator straight d x end fraction end cell row blank equals cell fraction numerator straight d open parentheses u to the power of negative 2 end exponent close parentheses over denominator straight d u end fraction cross times fraction numerator straight d open parentheses 3 x squared plus x minus 1 close parentheses over denominator straight d x end fraction end cell row blank equals cell open parentheses negative 2 u to the power of negative 3 end exponent close parentheses cross times open parentheses 3 times 2 times x to the power of 1 plus 1 close parentheses end cell row blank equals cell fraction numerator negative 2 over denominator u cubed end fraction cross times open parentheses 6 x plus 1 close parentheses end cell row blank equals cell fraction numerator negative 2 open parentheses 6 x plus 1 close parentheses over denominator open parentheses 3 x squared plus x minus 1 close parentheses end fraction end cell row cell fraction numerator straight d y over denominator straight d x end fraction end cell equals cell fraction numerator negative 12 x minus 2 over denominator 3 x squared plus x minus 1 end fraction end cell end table end style 

Jadi, diperoleh begin mathsize 14px style fraction numerator straight d y over denominator straight d x end fraction equals fraction numerator negative 12 x minus 2 over denominator 3 x squared plus x minus 1 end fraction end style.

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