Jika f(2x+4)=36x−1,x>61 dan f (x) menyatakan turunan pertama dari f(x), maka nilai dari 2f (4)= ….

Pertanyaan

Jika $\style{font-size:14px}{\mathrm f(2\mathrm x+4)=\sqrt[3]{6\mathrm x-1},\mathrm x>\frac16}$ dan $\style{font-size:14px}{f^\;(x)}$ menyatakan turunan pertama dari $\style{font-size:14px}{\mathrm f(\mathrm x)}$ , maka nilai dari $\style{font-size:14px}{2\mathrm f^\;(4)=}$ ….

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Jawaban

jawabannya adalah E.

Pembahasan

Misalkan:

Maka diperoleh fungsi sebagai berikut.

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Sehingga,

Misalkan:

Kemudian, hitung turunan pertama

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis end cell equals cell straight u to the power of 1 third end exponent end cell row cell straight f to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell 1 third straight u to the power of 1 third minus 1 end exponent times straight u to the power of apostrophe end cell row blank equals cell 1 third straight u to the power of negative 2 over 3 end exponent times 3 end cell row blank equals cell 1 over straight u to the power of begin display style 2 over 3 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator cube root of left parenthesis 3 straight x minus 13 right parenthesis squared end root end fraction end cell end table end style$

Jadi, diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight f to the power of apostrophe left parenthesis 4 right parenthesis end cell equals cell 2 times fraction numerator 1 over denominator cube root of left parenthesis 3 left parenthesis 4 right parenthesis minus 13 right parenthesis squared end root end fraction end cell row blank equals cell fraction numerator 2 over denominator cube root of left parenthesis negative 1 right parenthesis squared end root end fraction end cell row blank equals cell 2 over 1 end cell row blank equals 2 end table end style$

Jadi, jawabannya adalah E.