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Tentukan turunan fungsi-fungsi berikut.

Tentukan turunan fungsi-fungsi berikut.

begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator open parentheses x squared plus 2 x minus 3 close parentheses over denominator open parentheses x squared plus 5 close parentheses end fraction end style

Jawaban:

Sifat: Jika begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator u open parentheses x close parentheses over denominator v open parentheses x close parentheses end fraction end style, maka begin mathsize 14px style f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe open parentheses x close parentheses times v open parentheses x close parentheses minus u open parentheses x close parentheses times v apostrophe open parentheses x close parentheses over denominator v squared open parentheses x close parentheses end fraction end style

Turunan fungsi dari begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator open parentheses x squared plus 2 x minus 3 close parentheses over denominator open parentheses x squared plus 5 close parentheses end fraction end style adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator open parentheses 2 x plus 2 close parentheses open parentheses x squared plus 5 close parentheses minus open parentheses x squared plus 2 x minus 3 close parentheses open parentheses 2 x close parentheses over denominator open parentheses x squared plus 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x cubed plus 2 x squared plus 10 x plus 10 minus open parentheses 2 x cubed plus 4 x squared minus 6 x close parentheses over denominator open parentheses x squared plus 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 2 x squared plus 16 x plus 10 over denominator open parentheses x squared plus 5 close parentheses squared end fraction end cell end table end style

Dengan demikian, turunan fungsi tersebut adalah begin mathsize 14px style f apostrophe open parentheses x close parentheses equals fraction numerator negative 2 x squared plus 16 x plus 10 over denominator open parentheses x squared plus 5 close parentheses squared end fraction end style 

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