Pertanyaan

Tentukan turunan pertama fungsi berikut dengan menggunakan aturan turunan (penjumlahan, pengurangan, perkalian, pembagian, dan aturan rantai turunan) b. f ( x ) = 2 1 x 3 2 − 3 2 x 4 3

Tentukan turunan pertama fungsi berikut dengan menggunakan aturan turunan (penjumlahan, pengurangan, perkalian, pembagian, dan aturan rantai turunan)

b. $f (x) = \frac{1}{2} x^{\frac{2}{3}} - \frac{2}{3} x^{\frac{3}{4}}$

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Jawaban terverifikasi

Jawaban

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$table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 3 cube root of x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 2 fourth root of x end fraction end cell end table$ .

Pembahasan

Dengan menggunakan konsep dan rumus turunan fungssi aljabar diperoleh Dengan demikian .

Dengan menggunakan konsep dan rumus turunan fungssi aljabar diperoleh

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 1 half x to the power of 2 over 3 end exponent minus 2 over 3 x to the power of 3 over 4 end exponent end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell 1 half times 2 over 3 times x to the power of 2 over 3 minus 1 end exponent minus 2 over 3 times 3 over 4 x to the power of 3 over 4 minus 1 end exponent end cell row blank equals cell 1 third x to the power of negative 1 third end exponent minus 1 half x to the power of negative 1 fourth end exponent end cell row blank equals cell fraction numerator 1 over denominator 3 x to the power of begin display style 1 third end style end exponent end fraction minus fraction numerator 1 over denominator 2 x to the power of begin display style 1 fourth end style end exponent end fraction end cell row blank equals cell fraction numerator 1 over denominator 3 cube root of x end fraction minus fraction numerator 1 over denominator 2 fourth root of x end fraction end cell end table$

Dengan demikian $table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank apostrophe end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 3 cube root of x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 2 fourth root of x end fraction end cell end table$ .