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Carilah dxdy​ dari fungsi-fungsi berikut! y=(x−3)32​(x2+x+1)

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 minus 3 close parentheses to the power of bevelled 2 over 3 end exponent open parentheses x squared plus x plus 1 close parentheses end style

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

 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 minus 3 close parentheses to the power of bevelled 2 over 3 end exponent open parentheses x squared plus x plus 1 close parentheses end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank y 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 equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 over denominator 3 cube root of open parentheses x minus 3 close parentheses end root end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x squared plus x plus 1 close parentheses 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 cube root of left parenthesis x minus 3 right parenthesis squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 x plus 1 close parentheses end cell end table 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 minus 3 close parentheses to the power of bevelled 2 over 3 end exponent open parentheses x squared plus x plus 1 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 2 over 3 open parentheses x minus 3 close parentheses to the power of negative bevelled 1 third end exponent open parentheses x squared plus x plus 1 close parentheses plus open parentheses x minus 3 close parentheses to the power of bevelled 2 over 3 end exponent open parentheses 2 x plus 1 close parentheses end cell row blank equals cell fraction numerator 2 over denominator 3 cube root of open parentheses x minus 3 close parentheses end root end fraction open parentheses x squared plus x plus 1 close parentheses plus cube root of left parenthesis x minus 3 right parenthesis squared end root open parentheses 2 x plus 1 close parentheses 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 minus 3 close parentheses to the power of bevelled 2 over 3 end exponent open parentheses x squared plus x plus 1 close parentheses end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank y 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 equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 2 over denominator 3 cube root of open parentheses x minus 3 close parentheses end root end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x squared plus x plus 1 close parentheses 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 cube root of left parenthesis x minus 3 right parenthesis squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 x plus 1 close parentheses end cell end table end style

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

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