Pertanyaan

Carilah d x d y dari fungsi-fungsi berikut! y = ( x 2 + 3 ) ( 3 − 5 x 3 )

Carilah $\frac{d y}{d x}$ dari fungsi-fungsi berikut!

$y = (\frac{2}{x} + 3) (3 - \frac{3}{5 x})$

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

dari fungsi adalah

$begin mathsize 14px style fraction numerator d y over denominator d x end fraction end style$ dari fungsi $begin mathsize 14px style y equals open parentheses fraction numerator 2 over denominator square root of x end fraction plus 3 close parentheses open parentheses 3 minus fraction numerator 3 over denominator 5 square root of x end fraction close parentheses end style$ adalah $begin mathsize 14px style y apostrophe equals negative fraction numerator 21 over denominator 10 x square root of x end fraction plus fraction numerator 12 over denominator 10 x squared end fraction end style$

Pembahasan

Sifat turunan fungsi: Jika , maka turunannya adalah Turunan dari fungsi , yaitu Dengan demikian, dari fungsi adalah

Sifat turunan fungsi: Jika , maka turunannya adalah

Turunan dari fungsi $begin mathsize 14px style y equals open parentheses fraction numerator 2 over denominator square root of x end fraction plus 3 close parentheses open parentheses 3 minus fraction numerator 3 over denominator 5 square root of x end fraction close parentheses end style$ , yaitu

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe end cell equals cell negative fraction numerator 1 over denominator x square root of x end fraction open parentheses 3 minus fraction numerator 3 over denominator 5 square root of x end fraction close parentheses plus open parentheses fraction numerator 2 over denominator square root of x end fraction plus 3 close parentheses fraction numerator 3 over denominator 10 x square root of x end fraction end cell row blank equals cell negative fraction numerator 3 over denominator x square root of x end fraction plus fraction numerator 3 over denominator 5 x squared end fraction plus fraction numerator 6 over denominator 10 x squared end fraction plus fraction numerator 9 over denominator 10 x square root of x end fraction end cell row blank equals cell negative fraction numerator 21 over denominator 10 x square root of x end fraction plus fraction numerator 12 over denominator 10 x to the power of blank squared end exponent end fraction end cell end table end style$

Dengan demikian, $begin mathsize 14px style fraction numerator d y over denominator d x end fraction end style$ dari fungsi $begin mathsize 14px style y equals open parentheses fraction numerator 2 over denominator square root of x end fraction plus 3 close parentheses open parentheses 3 minus fraction numerator 3 over denominator 5 square root of x end fraction close parentheses end style$ adalah $begin mathsize 14px style y apostrophe equals negative fraction numerator 21 over denominator 10 x square root of x end fraction plus fraction numerator 12 over denominator 10 x squared end fraction end style$