Tentukan turunan dari fungsi-fungsi berikut. D. h(x)=6x−x3​+3

Pertanyaan

Tentukan turunan dari fungsi-fungsi berikut.

D. begin mathsize 14px style h open parentheses x close parentheses equals 6 x minus square root of x cubed end root plus 3 end style

  1. ...undefined 

  2. ...undefined 

D. Entry

Master Teacher

Jawaban terverifikasi

Jawaban

 turunan begin mathsize 14px style h open parentheses x close parentheses equals 6 x minus square root of x cubed end root plus 3 end style adalah begin mathsize 14px style h apostrophe left parenthesis x right parenthesis equals 6 minus fraction numerator 3 square root of x over denominator 2 end fraction end style.

Pembahasan

Ingat:

begin mathsize 14px style f open parentheses x close parentheses equals a x to the power of n end style, maka begin mathsize 14px style f apostrophe left parenthesis x right parenthesis equals fraction numerator d left parenthesis a x to the power of n right parenthesis over denominator d x end fraction equals a times n x to the power of n minus 1 end exponent end style.

Diketahui fungsi begin mathsize 14px style h open parentheses x close parentheses equals 6 x minus square root of x cubed end root plus 3 end style, maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell 6 x minus square root of x cubed end root plus 3 end cell row blank equals cell 6 x minus x to the power of 3 over 2 end exponent plus 3 end cell row cell h apostrophe left parenthesis x right parenthesis end cell equals cell 6 x to the power of 1 minus 1 end exponent minus open parentheses 3 over x x to the power of open parentheses 3 over 2 minus 1 close parentheses end exponent close parentheses plus 0 end cell row blank equals cell 6 x to the power of 0 minus 3 over 2 x to the power of 1 half end exponent end cell row blank equals cell 6 minus fraction numerator 3 square root of x over denominator 2 end fraction end cell end table end style 

Jadi, turunan begin mathsize 14px style h open parentheses x close parentheses equals 6 x minus square root of x cubed end root plus 3 end style adalah begin mathsize 14px style h apostrophe left parenthesis x right parenthesis equals 6 minus fraction numerator 3 square root of x over denominator 2 end fraction end style.

21

5.0 (1 rating)

Pertanyaan serupa

Tentukan turunan dari fungsi-fungsi berikut ini: f(x)=11+2x​−5x

19

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia