Pertanyaan

Jika f ( x ) = cos 5 ( 5 x − 4 ) ( 2 x 2 + 1 ) , maka nilai dari f ( 0 ) adalah ...

Jika $f (x) = cos^{5} (5 x - 4) (2 x^{2} + 1)$ , maka nilai dari $f (0)$ adalah ...

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Habis dalam

Klaim

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Pembahasan

Ingatlah! Maka, Cari turunan Cari turunan Maka, Cari n ilai Jadi,nilai dari adalah . Oleh karena itu, jawaban yang benar adalah E.

Ingatlah!

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f times g close parentheses apostrophe end cell equals cell f thin space apostrophe times g plus f times g apostrophe end cell row f equals cell cos to the power of 5 left parenthesis 5 x minus 4 right parenthesis end cell row g equals cell 2 x squared plus 1 end cell end table

Maka,

$begin mathsize 12px style fraction numerator d over denominator d x end fraction open parentheses cos to the power of 5 open parentheses 5 x minus 4 close parentheses open parentheses 2 x squared plus 1 close parentheses close parentheses equals fraction numerator d over denominator d x end fraction open parentheses cos to the power of 5 open parentheses 5 x minus 4 close parentheses close parentheses open parentheses 2 x squared plus 1 close parentheses plus fraction numerator d over denominator d x end fraction open parentheses 2 x squared plus 1 close parentheses cos to the power of 5 open parentheses 5 x minus 4 close parentheses end style$

Cari turunan $fraction numerator d over denominator d x end fraction open parentheses cos to the power of 5 open parentheses 5 x minus 4 close parentheses close parentheses$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction end cell equals cell fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row f equals cell u to the power of 5 end cell row u equals cell cos open parentheses 5 x minus 4 close parentheses end cell row blank blank blank row blank blank cell fraction numerator d over denominator d u end fraction open parentheses u to the power of 5 close parentheses fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses end cell row blank equals cell 5 u to the power of 5 minus 1 end exponent fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses end cell row blank equals cell 5 u to the power of 4 fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses end cell row blank equals cell 5 open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses to the power of 4 fraction numerator d over denominator d x end fraction open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses end cell row blank equals cell 5 open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses to the power of 4 fraction numerator d over denominator d u end fraction open parentheses cos open parentheses u close parentheses close parentheses fraction numerator d over denominator d x end fraction open parentheses 5 x minus 4 close parentheses end cell row blank equals cell 5 open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses to the power of 4 times negative sin open parentheses u close parentheses fraction numerator d over denominator d x end fraction open parentheses 5 x minus 4 close parentheses end cell row blank equals cell 5 open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses to the power of 4 times negative sin open parentheses 5 x minus 4 close parentheses fraction numerator d over denominator d x end fraction open parentheses 5 x minus 4 close parentheses end cell row blank equals cell 5 open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses to the power of 4 times negative sin open parentheses 5 x minus 4 close parentheses fraction numerator d over denominator d x end fraction open parentheses 5 x close parentheses minus fraction numerator d over denominator d x end fraction open parentheses 4 close parentheses end cell row blank equals cell 5 open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses to the power of 4 times negative sin open parentheses 5 x minus 4 close parentheses times 5 minus 0 end cell row blank equals cell 5 open parentheses cos open parentheses 5 x minus 4 close parentheses close parentheses to the power of 4 times negative sin open parentheses 5 x minus 4 close parentheses times 5 end cell row blank equals cell negative 25 cos to the power of 4 open parentheses 5 x minus 4 close parentheses sin open parentheses 5 x minus 4 close parentheses end cell end table$

Cari turunan $fraction numerator d over denominator d x end fraction open parentheses 2 x squared plus 1 close parentheses$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses 2 x squared plus 1 close parentheses end cell equals cell equals fraction numerator d over denominator d x end fraction open parentheses 2 x squared close parentheses plus fraction numerator d over denominator d x end fraction open parentheses 1 close parentheses end cell row blank equals cell 4 x plus 0 end cell row blank equals cell 4 x end cell end table$

Maka,

$begin mathsize 12px style fraction numerator d over denominator d x end fraction open parentheses cos to the power of 5 open parentheses 5 x minus 4 close parentheses open parentheses 2 x squared plus 1 close parentheses close parentheses equals negative 25 cos to the power of 4 open parentheses 5 x minus 4 close parentheses sin open parentheses 5 x minus 4 close parentheses open parentheses 2 x squared plus 1 close parentheses plus 4 x cos to the power of 5 open parentheses 5 x minus 4 close parentheses end style$

Cari n ilai f apostrophe left parenthesis 0 right parenthesis

Jadi, nilai dari f apostrophe left parenthesis 0 right parenthesis adalah negative 25 sin to the power of 4 left parenthesis negative 4 right parenthesis sin left parenthesis negative 4 right parenthesis .

Oleh karena itu, jawaban yang benar adalah E.