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Carilah dxdy​ dari fungsi-fungsi berikut! y=(x3−2x​)2(x2+3x−1)5

Pertanyaan

Carilah begin mathsize 14px style fraction numerator d y over denominator d x end fraction end style dari fungsi-fungsi berikut!

begin mathsize 14px style y equals open parentheses x cubed minus square root of 2 x end root close parentheses squared open parentheses x squared plus 3 x minus 1 close parentheses to the power of 5 end style

Pembahasan:

Sifat turunan fungsi: Jika begin mathsize 14px style f open parentheses x close parentheses equals u open parentheses x close parentheses times v open parentheses x close parentheses end style, maka turunannya adalah

begin mathsize 14px style f apostrophe open parentheses x close parentheses equals u apostrophe open parentheses x close parentheses times v open parentheses x close parentheses plus u open parentheses x close parentheses times v apostrophe open parentheses x close parentheses end style

Turunan dari fungsi begin mathsize 14px style y equals open parentheses x cubed minus square root of 2 x end root close parentheses squared open parentheses x squared plus 3 x minus 1 close parentheses to the power of 5 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 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 begin mathsize 14px style y equals open parentheses x cubed minus square root of 2 x end root close parentheses squared open parentheses x squared plus 3 x minus 1 close parentheses to the power of 5 end style 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

Jawaban terverifikasi

Dijawab oleh:

H. Eka

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 05 Oktober 2021

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Carilah dxdy​ dari fungsi-fungsi berikut! y=(2x−2)2(x+2)3(x2+1)

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