Pertanyaan

Carilah d x d y dari fungsi-fungsi berikut! y = ( x 3 − 2 x ) 2 ( x 2 + 3 x − 1 ) 5

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

$y = (x^{3} - 2 x)^{2} (x^{2} + 3 x - 1)^{5}$

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H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

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 , yaitu

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y apostrophe end cell equals cell 2 open parentheses x cubed minus square root of 2 x end root close parentheses open parentheses 3 x minus fraction numerator square root of 2 over denominator 2 square root of x end fraction close parentheses open parentheses x squared plus 3 x minus 1 close parentheses to the power of 5 end cell row blank blank cell plus open parentheses x cubed minus square root of 2 x end root close parentheses squared times 5 open parentheses x squared plus 3 x minus 1 close parentheses to the power of 4 open parentheses 2 x plus 3 close parentheses end cell row blank equals cell open parentheses x cubed minus square root of 2 x end root close parentheses open parentheses x squared plus 3 x minus 1 close parentheses to the power of 4 end cell row blank blank cell open square brackets 2 open parentheses 3 x minus fraction numerator square root of 2 over denominator 2 square root of x end fraction close parentheses open parentheses x squared plus 3 x minus 1 close parentheses plus 5 open parentheses x cubed minus square root of 2 x end root close parentheses open parentheses 2 x plus 3 close parentheses close square brackets end cell row blank equals cell open parentheses x cubed minus square root of 2 x end root close parentheses open parentheses x squared plus 3 x minus 1 close parentheses to the power of 4 end cell row blank blank cell open square brackets open parentheses 6 x minus fraction numerator square root of 2 over denominator square root of x end fraction close parentheses open parentheses x squared plus 3 x minus 1 close parentheses plus open parentheses x cubed minus square root of 2 x end root close parentheses open parentheses 10 x plus 15 close parentheses close square brackets end cell end table end style$

Dengan demikian, $begin mathsize 14px style fraction numerator d y over denominator d x end fraction end style$ dari fungsi adalah $begin mathsize 14px style y apostrophe equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x cubed minus square root of 2 x end root right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x squared plus 3 x minus 1 right parenthesis end cell end table to the power of 4 open square brackets open parentheses table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 2 over denominator square root of x end fraction end cell end table close parentheses table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x squared plus 3 x minus 1 right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x cubed minus square root of 2 x end root right parenthesis left parenthesis 10 x plus 15 right parenthesis end cell end table close square brackets end style$