Pertanyaan

Jika f x = x 2 +1 x - 3 maka nilai f'(1) = ....

Jika $begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x squared plus 1 over denominator x minus 3 end fraction end style$ maka nilai f'(1) = ....

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Habis dalam

Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

$u equals x squared plus 1 comma space maka straight space u to the power of apostrophe equals 2 x v equals x minus 3 comma space maka straight space v to the power of apostrophe equals 1 f to the power of apostrophe open parentheses x close parentheses equals fraction numerator u to the power of apostrophe v minus u v to the power of apostrophe over denominator v squared end fraction space space space space space space space equals fraction numerator open parentheses 2 x close parentheses open parentheses x minus 3 close parentheses minus open parentheses x squared plus 1 close parentheses open parentheses 1 close parentheses over denominator open parentheses x minus 3 close parentheses squared end fraction space space space space space space space equals fraction numerator left parenthesis 2 x squared minus 6 x right parenthesis minus left parenthesis x squared plus 1 right parenthesis over denominator open parentheses x minus 3 close parentheses squared end fraction space space space space space space space equals fraction numerator x squared minus 6 x minus 1 over denominator open parentheses x minus 3 close parentheses squared end fraction f to the power of apostrophe open parentheses 1 close parentheses equals fraction numerator left parenthesis 1 right parenthesis squared minus 6 left parenthesis 1 right parenthesis minus 1 over denominator open parentheses 1 minus 3 close parentheses squared end fraction space space space space space space space space equals fraction numerator negative 6 over denominator 4 end fraction equals negative 3 over 2$