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Pertanyaan

Diketahui fungsi f left parenthesis x right parenthesis equals open parentheses 3 x squared plus 5 x minus 2 close parentheses times open parentheses x squared minus 4 close parentheses to the power of 5. Tentukan turunan dari fungsi tersebut!

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

turunannya adalah left parenthesis 6 x plus 5 right parenthesis times open parentheses x squared minus 4 close parentheses to the power of 5 plus 5 open parentheses x squared minus 4 close parentheses to the power of 4 times open parentheses 2 x close parentheses times open parentheses 3 x squared plus 5 x minus 2 close parentheses.

Pembahasan

Bentuk fungsi f left parenthesis x right parenthesis equals open parentheses 3 x squared plus 5 x minus 2 close parentheses times open parentheses x squared minus 4 close parentheses to the power of 5 dapat dilihat sebagai bentuk f left parenthesis x right parenthesis equals u left parenthesis x right parenthesis cross times v left parenthesis x right parenthesis.

Jika u left parenthesis x right parenthesis equals open parentheses 3 x squared plus 5 x minus 2 close parentheses, maka u apostrophe left parenthesis x right parenthesis equals 6 x plus 5.

Jika v left parenthesis x right parenthesis equals open parentheses x squared minus 4 close parentheses to the power of 5, maka v apostrophe left parenthesis x right parenthesis equals 5 open parentheses x squared minus 4 close parentheses to the power of 4 times open parentheses 2 x close parentheses.

Sehingga:


table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell u apostrophe left parenthesis x right parenthesis times v left parenthesis x right parenthesis plus v apostrophe left parenthesis x right parenthesis times u left parenthesis x right parenthesis end cell row blank equals cell left parenthesis 6 x plus 5 right parenthesis times open parentheses x squared minus 4 close parentheses to the power of 5 plus 5 open parentheses x squared minus 4 close parentheses to the power of 4 times open parentheses 2 x close parentheses times open parentheses 3 x squared plus 5 x minus 2 close parentheses end cell end table


Jadi, turunannya adalah left parenthesis 6 x plus 5 right parenthesis times open parentheses x squared minus 4 close parentheses to the power of 5 plus 5 open parentheses x squared minus 4 close parentheses to the power of 4 times open parentheses 2 x close parentheses times open parentheses 3 x squared plus 5 x minus 2 close parentheses.

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