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Turunan pertama dari fungsi f open parentheses x close parentheses equals fraction numerator 5 x minus 6 over denominator 3 x plus 5 end fraction comma space x not equal to negative 5 over 3 adalah f apostrophe open parentheses x close parentheses equals horizontal ellipsis 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

turunan pertama dari f(x) adalah f apostrophe open parentheses x close parentheses equals 43 over left parenthesis 3 x plus 5 right parenthesis squared.

Pembahasan

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell u over v end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end cell row blank blank blank end table 

Dari f open parentheses x close parentheses equals fraction numerator 5 x minus 6 over denominator 3 x plus 5 end fraction comma space x not equal to negative 5 over 3diketahui bahwa:

u equals 5 x minus 6 dan v equals 3 x plus 5

u apostrophe equals 5 dan v apostrophe equals 3

Maka, 

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 u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator 5 times left parenthesis 3 x plus 5 right parenthesis minus left parenthesis 5 x minus 6 right parenthesis times 3 over denominator left parenthesis 3 x plus 5 right parenthesis squared end fraction end cell row blank equals cell fraction numerator left parenthesis 15 x plus 25 right parenthesis minus left parenthesis 15 x minus 18 right parenthesis over denominator left parenthesis 3 x plus 5 right parenthesis squared end fraction end cell row blank equals cell fraction numerator 25 minus left parenthesis negative 18 right parenthesis over denominator left parenthesis 3 x plus 5 right parenthesis squared end fraction end cell row blank equals cell 43 over left parenthesis 3 x plus 5 right parenthesis squared end cell end table

Dengan demikian, turunan pertama dari f(x) adalah f apostrophe open parentheses x close parentheses equals 43 over left parenthesis 3 x plus 5 right parenthesis squared.

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