Pertanyaan

Tentukan turunan dari fungsi-fungsi aijabar berikut. f. h ( x ) = 4 ( 3 x 2 − 1 ) 3

Tentukan turunan dari fungsi-fungsi aijabar berikut.

f. $h (x) = 4 (3 x^{2} - 1)^{3}$

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

turunan dari adalah .

turunan dari h left parenthesis x right parenthesis equals fourth root of open parentheses 3 x squared minus 1 close parentheses cubed end root

adalah $h apostrophe left parenthesis x right parenthesis equals fraction numerator 9 x over denominator 2 open parentheses 3 x squared minus 1 close parentheses to the power of 1 fourth end exponent end fraction$ .

Pembahasan

Ingatlah! Maka, Cari turunan dari . Maka, Subtitusikan . Cari turunan dari . Maka, Jadi, turunan dari adalah .

Ingatlah!

$fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction equals fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row f equals cell fourth root of u end cell row cell thin space u end cell equals cell open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses end cell row cell fraction numerator d over denominator d x end fraction open parentheses fourth root of open parentheses 3 x squared minus 1 close parentheses cubed end root close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses fourth root of u close parentheses fraction numerator d over denominator d x end fraction open parentheses open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses close parentheses end cell end table$

Cari turunan dari $fraction numerator d over denominator d u end fraction open parentheses fourth root of u close parentheses$ .

$table attributes columnalign right center left columnspacing 0px end attributes row cell n-th root of a end cell equals cell a to the power of 1 over n end exponent end cell row cell fraction numerator d over denominator d u end fraction open parentheses fourth root of u close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses u to the power of 1 fourth end exponent close parentheses end cell row blank equals cell 1 fourth u to the power of 1 fourth minus 1 end exponent end cell row blank equals cell 1 fourth u to the power of 1 fourth minus 4 over 4 end exponent end cell row blank equals cell 1 fourth u to the power of negative 3 over 4 end exponent end cell row blank equals cell 1 fourth times 1 over u to the power of 3 over 4 end exponent end cell row blank equals cell fraction numerator 1 times thin space 1 over denominator 4 u to the power of 3 over 4 end exponent end fraction end cell row blank equals cell fraction numerator 1 over denominator 4 u to the power of 3 over 4 end exponent end fraction end cell end table$

Maka,

Subtitusikan u equals open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses .

Cari turunan dari $fraction numerator d over denominator d x end fraction open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses$ .

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d f left parenthesis u right parenthesis over denominator d x end fraction end cell equals cell fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction end cell row f equals cell u cubed end cell row u equals cell open parentheses 3 x squared minus 1 close parentheses end cell row cell fraction numerator d over denominator d x end fraction open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses u cubed close parentheses fraction numerator d over denominator d x end fraction open parentheses open parentheses 3 x squared minus 1 close parentheses close parentheses end cell row blank equals cell 3 u to the power of 3 minus 1 end exponent open parentheses fraction numerator d over denominator d x end fraction open parentheses 3 x squared close parentheses minus fraction numerator d over denominator d x end fraction open parentheses 1 close parentheses close parentheses end cell row blank equals cell 3 u squared open parentheses fraction numerator d over denominator d x end fraction open parentheses 3 x squared close parentheses minus fraction numerator d over denominator d x end fraction open parentheses 1 close parentheses close parentheses end cell row blank equals cell 3 u squared open parentheses 3 fraction numerator d over denominator d x end fraction open parentheses x squared close parentheses minus 0 close parentheses end cell row blank equals cell 3 u squared open parentheses 3 open parentheses 2 x to the power of 2 minus 1 end exponent close parentheses minus 0 close parentheses end cell row blank equals cell 3 u squared open parentheses 3 open parentheses 2 x close parentheses minus 0 close parentheses end cell row blank equals cell 3 u squared open parentheses 6 x close parentheses end cell row blank equals cell 3 open parentheses 3 x squared minus 1 close parentheses squared times thin space 6 x end cell row blank equals cell 18 x open parentheses 3 x squared minus 1 close parentheses squared end cell end table$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses fourth root of open parentheses 3 x squared minus 1 close parentheses cubed end root close parentheses end cell equals cell fraction numerator d over denominator d u end fraction open parentheses fourth root of u close parentheses fraction numerator d over denominator d x end fraction open parentheses open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses close parentheses end cell row blank equals cell fraction numerator 1 over denominator 4 u to the power of 3 over 4 end exponent end fraction fraction numerator d over denominator d x end fraction open parentheses open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses close parentheses end cell row blank equals cell fraction numerator 1 over denominator 4 open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses to the power of 3 over 4 end exponent end fraction fraction numerator d over denominator d x end fraction open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses end cell row blank equals cell fraction numerator 1 over denominator 4 open parentheses open parentheses 3 x squared minus 1 close parentheses cubed close parentheses to the power of 3 over 4 end exponent end fraction times thin space 18 x open parentheses 3 x squared minus 1 close parentheses squared end cell row blank equals cell 1 over open parentheses 3 x squared minus 1 close parentheses to the power of 3 times 3 over 4 end exponent times thin space 18 x open parentheses 3 x squared minus 1 close parentheses squared end cell row blank equals cell 1 over open parentheses 3 x squared minus 1 close parentheses to the power of 9 over 4 end exponent times thin space 18 x open parentheses 3 x squared minus 1 close parentheses squared end cell row blank equals cell 18 times fraction numerator 1 over denominator 4 open parentheses 3 x squared minus 1 close parentheses to the power of 9 over 4 end exponent end fraction x open parentheses 3 x squared minus 1 close parentheses squared end cell row blank equals cell fraction numerator 1 times thin space 18 x open parentheses 3 x squared minus 1 close parentheses squared over denominator 4 open parentheses 3 x squared minus 1 close parentheses to the power of 9 over 4 end exponent end fraction end cell row blank equals cell fraction numerator 9 x open parentheses 3 x squared minus 1 close parentheses squared over denominator 2 open parentheses 3 x squared minus 1 close parentheses to the power of 9 over 4 end exponent end fraction end cell row blank equals cell fraction numerator 9 x over denominator 2 open parentheses 3 x squared minus 1 close parentheses to the power of 9 over 4 minus 2 end exponent end fraction end cell row blank equals cell fraction numerator 9 x over denominator 2 open parentheses 3 x squared minus 1 close parentheses to the power of 9 over 4 minus begin display style 8 over 4 end style end exponent end fraction end cell row blank equals cell fraction numerator 9 x over denominator 2 open parentheses 3 x squared minus 1 close parentheses to the power of 1 fourth end exponent end fraction end cell end table$

Jadi, turunan dari h left parenthesis x right parenthesis equals fourth root of open parentheses 3 x squared minus 1 close parentheses cubed end root adalah $h apostrophe left parenthesis x right parenthesis equals fraction numerator 9 x over denominator 2 open parentheses 3 x squared minus 1 close parentheses to the power of 1 fourth end exponent end fraction$ .