Pertanyaan

Bila f ( x ) = 2 + x − x 2 + 6 + 8 , maka f ( x ) adalah ...

Bila $f (x) = \frac{- x ^{2} + 6}{2 + x} + 8$ , maka $f (x)$ adalah ... $\;$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative x squared minus 4 x minus 6 over denominator open parentheses 2 plus x close parentheses squared end fraction end cell end table$ .

Pembahasan

Ingat! Keterangan: Diketahui , maka: Sehingga, turunan pertama fungsi adalah: Jadi, .

Ingat!

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell u over v end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction end cell row y equals cell a x to the power of n plus c end cell row cell y apostrophe end cell equals cell n a x to the power of n minus 1 end exponent end cell end table$

Keterangan:

Diketahui $f open parentheses x close parentheses equals fraction numerator negative x squared plus 6 over denominator 2 plus x end fraction plus 8$ , maka:

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell negative x squared plus 6 end cell row cell u apostrophe end cell equals cell negative 2 x end cell row v equals cell 2 plus x end cell row cell v apostrophe end cell equals 1 end table

Sehingga, turunan pertama fungsi f open parentheses x close parentheses adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator u apostrophe times v minus u times v apostrophe over denominator v squared end fraction plus 0 end cell row blank equals cell fraction numerator negative 2 x open parentheses 2 plus x close parentheses minus open parentheses negative x squared plus 6 close parentheses times 1 over denominator open parentheses 2 plus x close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 4 x minus 2 x squared plus x squared minus 6 over denominator open parentheses 2 plus x close parentheses squared end fraction end cell row blank equals cell fraction numerator negative x squared minus 4 x minus 6 over denominator open parentheses 2 plus x close parentheses squared end fraction end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative x squared minus 4 x minus 6 over denominator open parentheses 2 plus x close parentheses squared end fraction end cell end table$ .

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