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Turunan dari f ( x ) = 3 cos 2 ( 3 x 2 + 5 x ) adalah...

Turunan dari $f (x) = 3 cos^{2} (3 x^{2} + 5 x)$ adalah...

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Klaim

A. Nadhira

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$begin mathsize 12px style f left parenthesis x right parenthesis equals cos to the power of 2 over 3 end exponent left parenthesis 3 x squared plus 5 x right parenthesis f apostrophe left parenthesis x right parenthesis equals 2 over 3 cos to the power of negative 1 third end exponent left parenthesis 3 x squared plus 5 x right parenthesis open square brackets negative sin open parentheses 3 x squared plus 5 x close parentheses close square brackets left parenthesis 6 x plus 5 right parenthesis f apostrophe left parenthesis x right parenthesis equals negative 2 over 3 left parenthesis 6 x plus 5 right parenthesis fraction numerator sin open parentheses 3 x squared plus 5 x close parentheses over denominator cos to the power of begin display style 1 third end style end exponent left parenthesis 3 x squared plus 5 x right parenthesis end fraction cross times fraction numerator cos left parenthesis 3 x squared plus 5 x right parenthesis over denominator cos open parentheses 3 x squared plus 5 x close parentheses end fraction f apostrophe left parenthesis x right parenthesis equals negative 2 over 3 left parenthesis 6 x plus 5 right parenthesis fraction numerator sin open parentheses 3 x squared plus 5 x close parentheses over denominator cos open parentheses 3 x squared plus 5 x close parentheses end fraction cross times fraction numerator cos open parentheses 3 x squared plus 5 x close parentheses over denominator cos to the power of begin display style 1 third end style end exponent left parenthesis 3 x squared plus 5 x right parenthesis end fraction f apostrophe left parenthesis x right parenthesis equals negative 2 over 3 left parenthesis 6 x plus 5 right parenthesis tan open parentheses 3 x squared plus 5 x close parentheses cos to the power of 2 over 3 end exponent left parenthesis 3 x squared plus 5 x right parenthesis f apostrophe left parenthesis x right parenthesis equals negative 2 over 3 left parenthesis 6 x plus 5 right parenthesis tan open parentheses 3 x squared plus 5 x close parentheses cube root of cos squared left parenthesis 3 x squared plus 5 x right parenthesis end root end style$