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Dengan menggunakan konsep turunan, tentukan turunan dari fungsi-fungsi berikut.

 

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F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Rumus turunan pada perkalian dua fungsi: begin mathsize 14px style f open parentheses x close parentheses equals u times v end style, maka begin mathsize 14px style f to the power of apostrophe open parentheses x close parentheses equals u to the power of apostrophe times v plus u times v to the power of apostrophe end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 2 x squared end cell row cell u to the power of apostrophe end cell equals cell 4 x end cell row v equals cell open parentheses negative 3 x plus 1 close parentheses cubed end cell row cell v to the power of apostrophe end cell equals cell 3 open parentheses negative 3 x plus 1 close parentheses squared times left parenthesis negative 3 right parenthesis end cell row blank equals cell negative 9 open parentheses negative 3 x plus 1 close parentheses squared end cell end table end style

Substitusikan ke dalam rumus:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of apostrophe left parenthesis x right parenthesis end cell equals cell 4 x times open parentheses negative 3 x plus 1 close parentheses cubed plus 2 x squared times left parenthesis negative 9 open parentheses negative 3 x plus 1 close parentheses squared right parenthesis end cell row blank equals cell 4 x times open parentheses negative 3 x plus 1 close parentheses cubed minus 18 x squared times open parentheses negative 3 x plus 1 close parentheses squared end cell end table end style

Jadi turunan dari begin mathsize 14px style f open parentheses x close parentheses equals 2 x squared times open parentheses negative 3 x plus 1 close parentheses cubed end style adalah begin mathsize 14px style f to the power of apostrophe left parenthesis x right parenthesis equals 4 x times open parentheses negative 3 x plus 1 close parentheses cubed minus 18 x squared times open parentheses negative 3 x plus 1 close parentheses squared end style

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