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Dengan menggunakan konsep turunan, tentukan turuna...

Dengan menggunakan konsep turunan, tentukan turunan dari fungsi berikut.

f. begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 x minus 3 end root end cell end table end style

Jawaban:

Ingat!

Aturan Rantai:

begin mathsize 14px style y equals open parentheses g open parentheses x close parentheses close parentheses to the power of n comma space maka space y apostrophe equals n times open parentheses g open parentheses x close parentheses close parentheses to the power of n minus 1 end exponent times g apostrophe left parenthesis x right parenthesis end style 

Dengan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fungsi space awal end cell row cell y apostrophe end cell equals cell turunan space pertama space fungsi space y end cell row cell g open parentheses x close parentheses end cell equals cell fungsi space yang space dipangkatkan end cell row cell g apostrophe open parentheses x close parentheses end cell equals cell turunan space pertama space fungsi space g left parenthesis x right parenthesis end cell end table end style 

Diketahui begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 2 x minus 3 end root end cell end table end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 3 end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals cell 2 x to the power of 1 minus 1 end exponent minus 0 end cell row cell g apostrophe left parenthesis x right parenthesis end cell equals 2 end table end style    

Sehingga turunan fungsi tersebut:

    begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell square root of 2 x minus 3 end root end cell row cell f left parenthesis x right parenthesis end cell equals cell open parentheses 2 x minus 3 close parentheses to the power of 1 half end exponent end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell n open parentheses g open parentheses x close parentheses close parentheses to the power of n minus 1 end exponent times g apostrophe left parenthesis x right parenthesis end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 1 half open parentheses 2 x minus 3 close parentheses to the power of 1 half minus 1 end exponent times 2 end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell open parentheses 2 x minus 3 close parentheses to the power of negative 1 half end exponent end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 1 over open parentheses 2 x minus 3 close parentheses to the power of begin display style 1 half end style end exponent end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 1 over denominator square root of 2 x minus 3 end root end fraction end cell end table end style 

Jadi, turunan fungsi tersebut adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator square root of 2 x minus 3 end root end fraction end cell end table end style.

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