Pertanyaan

Jika f ( x ) = x 2 + 1 x maka f ( 2 ) = ...

Jika $f (x) = \frac{x}{x ^{2} + 1}$ maka $f (2) = ...$

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

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f apostrophe left parenthesis 2 right parenthesis equals negative 3 over 25

Pembahasan

Pada turunan berlaku aturan sebagai berikut. Dengan, dan Maka, Sehingga di dapat turunan dari adalah , kemudian mencari dengan subtitusi . Jadi, .

Pada turunan berlaku aturan sebagai berikut.

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

Dengan, u equals x dan v equals x squared plus 1 Maka,

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

Sehingga di dapat turunan dari $f left parenthesis x right parenthesis equals fraction numerator x over denominator x squared plus 1 end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f apostrophe left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus x squared over denominator x to the power of 4 plus 2 x squared plus 1 end fraction end cell end table$ , kemudian mencari f apostrophe left parenthesis 2 right parenthesis dengan subtitusi x equals 2 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 1 minus x squared over denominator x to the power of 4 plus 2 x squared plus 1 end fraction end cell row cell f apostrophe left parenthesis 2 right parenthesis end cell equals cell fraction numerator 1 minus open parentheses 2 close parentheses squared over denominator open parentheses 2 close parentheses to the power of 4 plus 2 open parentheses 2 close parentheses squared plus 1 end fraction end cell row cell f apostrophe left parenthesis 2 right parenthesis end cell equals cell fraction numerator 1 minus 4 over denominator 16 plus 2 open parentheses 4 close parentheses plus 1 end fraction end cell row cell f apostrophe left parenthesis 2 right parenthesis end cell equals cell fraction numerator negative 3 over denominator 16 plus 8 plus 1 end fraction end cell row cell f apostrophe left parenthesis 2 right parenthesis end cell equals cell fraction numerator negative 3 over denominator 25 end fraction end cell end table$

Jadi, f apostrophe left parenthesis 2 right parenthesis equals negative 3 over 25 .