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Tentukan turunan pertama ( d x d y ​ ) dari fungsi berikut. b. x 2 y 2 + 9 y = x 2 + 13

Tentukan turunan pertama  dari fungsi berikut.

b.  

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Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

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diperoleh .

diperoleh begin mathsize 14px style fraction numerator straight d y over denominator straight d x end fraction equals fraction numerator 2 x minus 2 x y squared over denominator 2 x squared y plus 9 end fraction end style.

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Pembahasan

Gunakan konsep aturan perkalian dua fungsi sebagai berikut: Akan ditentukan turunan pertama dari fungsi ,perhatikan perhitungan berikut: Jadi, diperoleh .

Gunakan konsep aturan perkalian dua fungsi sebagai berikut:

 begin mathsize 14px style f open parentheses x close parentheses equals u times v rightwards double arrow f apostrophe open parentheses x close parentheses equals u apostrophe v plus u v apostrophe f open parentheses x close parentheses equals u plus-or-minus v rightwards double arrow f apostrophe open parentheses x close parentheses equals u apostrophe plus-or-minus v apostrophe end style 

Akan ditentukan turunan pertama undefined dari fungsi begin mathsize 14px style x squared y squared plus 9 y equals x squared plus 13 end style, perhatikan perhitungan berikut:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell x squared y squared plus 9 y end cell equals cell x squared plus 13 end cell row cell fraction numerator straight d over denominator straight d x end fraction open parentheses x squared y squared close parentheses plus fraction numerator straight d over denominator straight d x end fraction open parentheses 9 y close parentheses end cell equals cell fraction numerator straight d over denominator straight d x end fraction open parentheses x squared close parentheses plus fraction numerator straight d over denominator straight d x end fraction open parentheses 13 close parentheses end cell row cell fraction numerator straight d over denominator straight d x end fraction open parentheses x squared close parentheses cross times y squared plus x squared cross times fraction numerator straight d over denominator straight d x end fraction open parentheses y squared close parentheses plus 9 fraction numerator straight d y over denominator straight d x end fraction end cell equals cell 2 x plus 0 end cell row cell 2 x y squared plus x squared cross times 2 y cross times fraction numerator straight d y over denominator straight d x end fraction plus 9 fraction numerator straight d y over denominator straight d x end fraction end cell equals cell 2 x end cell row cell 2 x y squared plus 2 x squared y cross times fraction numerator straight d y over denominator straight d x end fraction plus 9 cross times fraction numerator straight d y over denominator straight d x end fraction end cell equals cell 2 x end cell row cell 2 x squared y cross times fraction numerator straight d y over denominator straight d x end fraction plus 9 cross times fraction numerator straight d y over denominator straight d x end fraction end cell equals cell 2 x minus 2 x y squared end cell row cell open parentheses 2 x squared y plus 9 close parentheses fraction numerator straight d y over denominator straight d x end fraction end cell equals cell 2 x minus 2 x y squared end cell row cell fraction numerator straight d y over denominator straight d x end fraction end cell equals cell fraction numerator 2 x minus 2 x y squared over denominator 2 x squared y plus 9 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 2 x minus 2 x y squared over denominator 2 x squared y plus 9 end fraction end style.

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