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Diketahui , jika menyatakan turunan pertama . Maka

Pertanyaan

Diketahui f open parentheses x close parentheses equals fraction numerator x squared plus 3 over denominator 2 x plus 1 end fraction, jika f apostrophe open parentheses x close parentheses menyatakan turunan pertama f open parentheses x close parentheses. Maka f open parentheses 0 close parentheses plus 2 f apostrophe open parentheses 0 close parentheses equals...

  1. negative 10

  2. negative 9

  3. negative 7

  4. negative 5

  5. negative 3

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator x squared plus 3 over denominator 2 x plus 1 end fraction end cell row blank blank cell M i s a l colon end cell row n equals cell x squared plus 3 rightwards arrow n apostrophe equals 2 x end cell row m equals cell 2 x plus 1 rightwards arrow m apostrophe equals 2 end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator n apostrophe m minus m apostrophe n over denominator m squared end fraction end cell row blank equals cell fraction numerator open parentheses 2 x close parentheses open parentheses 2 x plus 1 close parentheses minus 2 open parentheses x squared plus 3 close parentheses over denominator open parentheses 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 4 x squared plus 2 x minus 2 x squared minus 6 over denominator open parentheses 2 x plus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x squared plus 2 x minus 6 over denominator open parentheses 2 x plus 1 close parentheses squared end fraction end cell row cell f open parentheses 0 close parentheses plus 2 f apostrophe open parentheses 0 close parentheses end cell equals cell fraction numerator x squared plus 3 over denominator 2 x plus 1 end fraction plus 2 open parentheses fraction numerator 2 x squared plus 2 x minus 6 over denominator open parentheses 2 x plus 1 close parentheses squared end fraction close parentheses end cell row blank equals cell fraction numerator open parentheses 0 close parentheses squared plus 3 over denominator 2 open parentheses 0 close parentheses plus 1 end fraction plus 2 open parentheses fraction numerator 2 open parentheses 0 close parentheses squared plus 2 open parentheses 0 close parentheses minus 6 over denominator open parentheses 2 open parentheses 0 close parentheses plus 1 close parentheses squared end fraction close parentheses end cell row blank equals cell 3 plus 2 open parentheses negative 6 close parentheses end cell row blank equals cell 3 minus 12 end cell row blank equals cell negative 9 end cell end table

Jadi, nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 0 close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 0 close parentheses 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 9 end table.

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Herlanda

Mahasiswa/Alumni STKIP PGRI Jombang

Terakhir diupdate 05 Juni 2021

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Pertanyaan yang serupa

Tentukan nilai dari pada nilai yang ditetapkan. b. ,  untuk

Pembahasan Soal:

Roboguru

Turunan pertama dari fungsi untuk  adalah...

Pembahasan Soal:

Penyelesaian :

y equals fraction numerator negative 5 x plus 1 over denominator 2 x plus 3 end fraction

Misal :

U = -5x + 1

U' = -5

v = 2x +3

V' =2

y equals U over V rightwards arrow y apostrophe equals fraction numerator U apostrophe V minus U V apostrophe over denominator V squared end fraction  Y apostrophe equals fraction numerator negative 5 left parenthesis 2 x plus 3 right parenthesis minus 2 left parenthesis negative 5 x plus l right parenthesis over denominator left parenthesis 2 x plus 3 right parenthesis squared end fraction  equals fraction numerator negative space 10 space minus space 15 plus space 10 x minus 2 over denominator left parenthesis 2 x plus 3 right parenthesis squared end fraction  equals fraction numerator negative 17 over denominator left parenthesis 2 x plus 3 right parenthesis squared end fraction

Roboguru

Tentukan turunan dari fungsi berikut.

Pembahasan Soal:

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator open parentheses 4 x minus 1 close parentheses over denominator open parentheses x squared plus 5 close parentheses end fraction end style, misalkan begin mathsize 14px style u equals 4 x minus 1 space dan space v equals x squared plus 5 end style, maka begin mathsize 14px style u apostrophe equals 4 space dan space v apostrophe equals 2 x end style, sehingga

begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator open parentheses 4 x minus 1 close parentheses over denominator open parentheses x squared plus 5 close parentheses end fraction f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction space space space space space space space space equals fraction numerator 4 open parentheses x squared plus 5 close parentheses minus 2 x open parentheses 4 x minus 1 close parentheses over denominator open parentheses x squared plus 5 close parentheses squared end fraction space space space space space space space space equals fraction numerator 4 x squared plus 20 minus 8 x squared plus 2 x over denominator x to the power of 4 plus 10 x squared plus 25 end fraction space space space space space space space space equals fraction numerator negative 4 x squared plus 2 x plus 20 over denominator x to the power of 4 plus 10 x squared plus 25 end fraction end style   


Jadi, turunan dari begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator open parentheses 4 x minus 1 close parentheses over denominator open parentheses x squared plus 5 close parentheses end fraction end style adalah

 begin mathsize 14px style f apostrophe open parentheses x close parentheses space equals fraction numerator negative 4 x squared plus 2 x plus 20 over denominator x to the power of 4 plus 10 x squared plus 25 end fraction end style.

Roboguru

Turunan dari  adalah ....

Pembahasan Soal:

Apabila suatu fungsi bentuknya adalah begin mathsize 14px style y equals u over v end style, maka begin mathsize 14px style y apostrophe equals fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end style.

Suatu fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x plus 5 over denominator 2 x plus 3 end fraction end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x plus 5 end cell row cell u apostrophe end cell equals 1 row v equals cell 2 x plus 3 end cell row cell v apostrophe end cell equals 2 end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses apostrophe 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 1 times open parentheses 2 x plus 3 close parentheses minus open parentheses x plus 5 close parentheses times 2 over denominator open parentheses 2 x plus 3 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x plus 3 minus open parentheses 2 x plus 10 close parentheses over denominator left parenthesis 2 x plus 3 right parenthesis squared end fraction end cell row blank equals cell fraction numerator up diagonal strike 2 x end strike plus 3 minus up diagonal strike 2 x end strike minus 10 over denominator left parenthesis 2 x plus 3 right parenthesis squared end fraction end cell row blank equals cell fraction numerator negative 7 over denominator left parenthesis 2 x plus 3 right parenthesis squared end fraction end cell end table end style  

Jadi, jawaban yang tepat adalah E.

Roboguru

Turunkan nilai dari  untuk nilai  yang ditetapkan. d.

Pembahasan Soal:

Roboguru

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