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Jika turunan pertama dari f(x) adalah f'(x) dan turunan kedua dari f(x) adalah f"(x), maka jika

Jika turunan pertama dari f(x) adalah f'(x) dan turunan kedua dari f(x) adalah f"(x), maka jika begin mathsize 14px style f left parenthesis x right parenthesis equals tan open parentheses sin open parentheses x close parentheses close parentheses comma space f apostrophe open parentheses straight pi over 3 close parentheses plus f " open parentheses straight pi over 3 close parentheses equals... end style

  1. begin mathsize 12px style left parenthesis 1 minus square root of 3 right parenthesis space s e c squared space open parentheses 1 half square root of 3 close parentheses space plus space s e c open parentheses 1 half square root of 3 close parentheses. tan squared open parentheses 1 half square root of 3 close parentheses end style

  2. begin mathsize 12px style open parentheses 1 half plus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction square root of 3 space close parentheses space s e c squared space open parentheses 1 half square root of 3 close parentheses space plus 1 half space s e c open parentheses 1 half square root of 3 close parentheses. tan squared open parentheses 1 half square root of 3 close parentheses end style

  3. begin mathsize 12px style open parentheses 1 half minus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction square root of 3 space close parentheses space s e c squared space open parentheses 1 half square root of 3 close parentheses space plus space s e c open parentheses 1 half square root of 3 close parentheses. tan squared open parentheses 1 half square root of 3 close parentheses end style

  4. begin mathsize 12px style open parentheses 1 half plus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction square root of 3 space close parentheses space s e c squared space open parentheses 1 half square root of 3 close parentheses space minus space s e c open parentheses 1 half square root of 3 close parentheses. tan squared open parentheses 1 half square root of 3 close parentheses end style

  5. begin mathsize 12px style open parentheses 1 plus square root of 3 space close parentheses space s e c squared space open parentheses 1 half square root of 3 close parentheses space plus space s e c open parentheses 1 half square root of 3 close parentheses. tan squared open parentheses 1 half square root of 3 close parentheses end style

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N. Ayu

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begin mathsize 12px style f apostrophe space left parenthesis x right parenthesis equals sec squared left parenthesis sin space x space right parenthesis. cos left parenthesis x right parenthesis comma space maka space space f apostrophe space open parentheses pi over 3 close parentheses equals sec squared space open parentheses sin invisible function application space open parentheses pi over 3 close parentheses close parentheses space space cos space open parentheses pi over 3 close parentheses space space space f apostrophe space open parentheses pi over 3 close parentheses equals sec squared open parentheses 1 half square root of 3 close parentheses space. space 1 half space space Kemudian space f apostrophe apostrophe space left parenthesis x right parenthesis equals u apostrophe space v plus u v apostrophe space f apostrophe apostrophe space left parenthesis x right parenthesis equals 2 space sec space left parenthesis sin space x space right parenthesis space. space tan squared left parenthesis sin space x space right parenthesis space. space cos squared space x plus sec squared space left parenthesis sin space x right parenthesis space. space sin space x space space f apostrophe apostrophe space open parentheses pi over 3 close parentheses equals 2 space sec space open parentheses 1 half square root of 3 close parentheses space. space tan squared space open parentheses 1 half square root of 3 close parentheses space. space open parentheses 1 half close parentheses squared plus sec to the power of 2 space end exponent open parentheses 1 half square root of 3 close parentheses space. space open parentheses 1 half square root of 3 close parentheses space space f apostrophe apostrophe space open parentheses pi over 3 close parentheses equals 1 half sec space open parentheses 1 half square root of 3 close parentheses space. space tan squared space open parentheses 1 half square root of 3 close parentheses plus 1 half square root of 3 space space sec to the power of 2 space end exponent open parentheses 1 half square root of 3 close parentheses space Jadi comma space f apostrophe space open parentheses pi over 3 close parentheses plus f apostrophe apostrophe space open parentheses pi over 3 close parentheses space equals s ec squared space open parentheses 1 half square root of 3 close parentheses.1 half plus 1 half sec space open parentheses 1 half square root of 3 close parentheses space. space tan squared space open parentheses 1 half square root of 3 close parentheses plus space 1 half square root of 3 space sec to the power of 2 space end exponent space open parentheses 1 half square root of 3 close parentheses space equals space open parentheses 1 half plus space 1 half square root of 3 close parentheses space sec to the power of 2 space end exponent open parentheses 1 half square root of 3 close parentheses plus 1 half sec space open parentheses 1 half square root of 3 close parentheses space. space tan squared space open parentheses 1 half square root of 3 close parentheses end style

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