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Dengan menggunakan konsep turunan tentukan turunan...

Dengan menggunakan konsep turunan tentukan turunan dari fungsi berikut:

begin mathsize 14px style F open parentheses x close parentheses equals x cubed open parentheses 2 x plus 1 close parentheses to the power of 5 end style 

Jawaban:

Diketahui begin mathsize 14px style F open parentheses x close parentheses equals x cubed open parentheses 2 x plus 1 close parentheses to the power of 5 end style, maka:

begin mathsize 14px style u equals x cubed rightwards arrow u apostrophe equals 3 x squared v equals open parentheses 2 x plus 1 close parentheses to the power of 5 rightwards arrow v apostrophe equals 5 times open parentheses 2 x plus 1 close parentheses to the power of 5 minus 1 end exponent times 2 equals 10 open parentheses 2 x plus 1 close parentheses to the power of 4 end style 

Sehingga:

begin mathsize 14px style F apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction F apostrophe open parentheses x close parentheses equals fraction numerator 3 x squared times open parentheses 2 x plus 1 close parentheses to the power of 5 minus x cubed times 10 open parentheses 2 x plus 1 close parentheses to the power of 4 over denominator open parentheses open parentheses 2 x plus 1 close parentheses to the power of 5 close parentheses squared end fraction F apostrophe open parentheses x close parentheses equals fraction numerator 3 x squared times open parentheses 2 x plus 1 close parentheses to the power of 5 minus x cubed times 10 open parentheses 2 x plus 1 close parentheses to the power of 4 over denominator open parentheses 2 x plus 1 close parentheses to the power of 10 end fraction end style 

Jadi, turunan dari fungsi ​​​​​​​begin mathsize 14px style F open parentheses x close parentheses equals x cubed open parentheses 2 x plus 1 close parentheses to the power of 5 end style adalah begin mathsize 14px style fraction numerator 3 x squared times open parentheses 2 x plus 1 close parentheses to the power of 5 minus x cubed times 10 open parentheses 2 x plus 1 close parentheses to the power of 4 over denominator open parentheses 2 x plus 1 close parentheses to the power of 10 end fraction end style.

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