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Turunan pertama dari  adalah

Turunan pertama dari begin mathsize 14px style f open parentheses x close parentheses equals open parentheses 4 x squared plus 3 close parentheses to the power of 5 open parentheses 2 x minus 3 close parentheses to the power of 4 end style adalah begin mathsize 14px style horizontal ellipsis end style 

Jawaban:

Misalkanbegin mathsize 14px style u left parenthesis x right parenthesis equals open parentheses 4 x squared plus 3 close parentheses to the power of 5 end style dan begin mathsize 14px style v left parenthesis x right parenthesis equals open parentheses 2 x minus 3 close parentheses to the power of 4 end style. Dengan menggunakan aturan rantai, turunan dari kedua fungsi tersebut adalah sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell u apostrophe left parenthesis x right parenthesis end cell equals cell 5 open parentheses 8 x close parentheses open parentheses 4 x squared plus 3 close parentheses to the power of 5 minus 1 end exponent end cell row blank equals cell 40 x open parentheses 4 x squared plus 3 close parentheses to the power of 4 end cell row cell v apostrophe left parenthesis x right parenthesis end cell equals cell 4 open parentheses 2 close parentheses open parentheses 2 x minus 3 close parentheses to the power of 4 minus 1 end exponent end cell row blank equals cell 8 open parentheses 2 x minus 3 close parentheses cubed end cell end table end style 

Turunan dari begin mathsize 14px style f left parenthesis x right parenthesis end style dapat dicari dengan menggunakan konsep turunan pada perkalian dua fungsi begin mathsize 14px style u left parenthesis x right parenthesis end style dan begin mathsize 14px style v left parenthesis x right parenthesis end style sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator d over denominator d x end fraction open parentheses u left parenthesis x right parenthesis times v left parenthesis x right parenthesis close parentheses end cell row blank equals cell u apostrophe left parenthesis x right parenthesis times v left parenthesis x right parenthesis plus u left parenthesis x right parenthesis times v apostrophe left parenthesis x right parenthesis end cell row blank equals cell open parentheses 40 x open parentheses 4 x squared plus 3 close parentheses to the power of 4 close parentheses open parentheses 2 x minus 3 close parentheses to the power of 4 plus open parentheses 4 x squared plus 3 close parentheses to the power of 5 open parentheses 8 open parentheses 2 x minus 3 close parentheses cubed close parentheses end cell row blank equals cell 40 x open parentheses 4 x squared plus 3 close parentheses to the power of 4 open parentheses 2 x minus 3 close parentheses to the power of 4 plus 8 open parentheses 4 x squared plus 3 close parentheses to the power of 5 open parentheses 2 x minus 3 close parentheses cubed end cell row blank equals cell 8 open parentheses 4 x squared plus 3 close parentheses to the power of 4 open parentheses 2 x minus 3 close parentheses cubed open parentheses 5 x open parentheses 2 x minus 3 close parentheses plus open parentheses 4 x squared plus 3 close parentheses close parentheses end cell row blank equals cell 8 open parentheses 4 x squared plus 3 close parentheses to the power of 4 open parentheses 2 x minus 3 close parentheses cubed open parentheses 10 x squared minus 15 x plus 4 x squared plus 3 close parentheses end cell row blank equals cell 8 open parentheses 4 x squared plus 3 close parentheses to the power of 4 open parentheses 2 x minus 3 close parentheses cubed open parentheses 14 x squared minus 15 x plus 3 close parentheses end cell end table end style 

Jadi, turunan kedua dari fungsi tersebut adalah Error converting from MathML to accessible text..

 

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