Roboguru

Diketahui f'(x) turunan pertama fungsi aljabar . Nilai f'(-3) adalah....

Pertanyaan

Diketahui f'(x) turunan pertama fungsi aljabar f open parentheses x close parentheses open parentheses 1 minus x close parentheses cubed over open parentheses 2 x plus 4 close parentheses squared semicolon x not equal to negative 2. Nilai f'(-3) adalah....

  1. 90

  2. 88

  3. 56 (2x +4)2

  4. 44

  5. 20

Pembahasan Soal:

Ingat bahwa :

f left parenthesis x right parenthesis equals u over v rightwards double arrow f apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction  u equals left parenthesis 1 minus x right parenthesis cubed  u apostrophe equals negative 3 left parenthesis 1 minus x right parenthesis squared  v equals left parenthesis 2 x plus 4 right parenthesis squared  v apostrophe equals 2 left parenthesis 2 x plus 4 right parenthesis left parenthesis 2 right parenthesis equals 8 x plus 16  M a k a comma  f apostrophe left parenthesis x right parenthesis equals fraction numerator negative 3 left parenthesis 1 minus x right parenthesis squared left parenthesis 2 x plus 4 right parenthesis squared minus left parenthesis 1 minus x right parenthesis cubed left parenthesis 8 x plus 16 right parenthesis over denominator left parenthesis 2 x plus 4 right parenthesis to the power of 4 end fraction  f apostrophe left parenthesis negative 3 right parenthesis equals fraction numerator negative 3 left parenthesis 1 plus 3 right parenthesis squared left parenthesis 2 left parenthesis negative 3 right parenthesis plus 4 right parenthesis squared minus left parenthesis 1 plus 3 right parenthesis cubed left parenthesis 8 left parenthesis negative 3 right parenthesis plus 16 right parenthesis over denominator left parenthesis 2 left parenthesis negative 3 right parenthesis plus 4 right parenthesis to the power of 4 end fraction  f apostrophe left parenthesis 3 right parenthesis equals fraction numerator negative 3 left parenthesis 4 right parenthesis squared left parenthesis negative 2 right parenthesis squared minus left parenthesis 4 right parenthesis cubed left parenthesis negative 8 right parenthesis over denominator left parenthesis negative 2 right parenthesis to the power of 4 end fraction  f apostrophe left parenthesis 3 right parenthesis equals 20

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Roy

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 17 Desember 2020

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Jika f(x)=x2−44x−2​ dan menyatakan turunan pertama

Pembahasan Soal:

Misalkan:

Maka:

 

 

 

Maka:

0

Roboguru

Jika , maka

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 4 x minus 1 over denominator 3 x plus 2 end fraction end style. Misalkan,

begin mathsize 14px style g left parenthesis x right parenthesis equals 4 x minus 1 rightwards arrow g apostrophe left parenthesis x right parenthesis equals 4 h left parenthesis x right parenthesis equals 3 x plus 2 rightwards arrow h apostrophe left parenthesis x right parenthesis equals 3 end style.

Turunan pertama dari fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style adalah,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator g left parenthesis x right parenthesis over denominator h left parenthesis x right parenthesis end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator g apostrophe left parenthesis x right parenthesis times h left parenthesis x right parenthesis minus g left parenthesis x right parenthesis times h apostrophe left parenthesis x right parenthesis over denominator h squared left parenthesis x right parenthesis end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 4 left parenthesis 3 x plus 2 right parenthesis minus left parenthesis 4 x minus 1 right parenthesis left parenthesis 3 right parenthesis over denominator left parenthesis 3 x plus 2 right parenthesis squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator 12 x plus 8 minus 12 x plus 3 over denominator left parenthesis 3 x plus 2 right parenthesis squared end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 11 over left parenthesis 3 x plus 2 right parenthesis squared end cell end table end style

Substitusikan x=0 ke dalam fungsi turunan, maka didapatkan

begin mathsize 14px style f apostrophe left parenthesis 0 right parenthesis equals 11 over left parenthesis 3 times 0 plus 2 right parenthesis squared equals 11 over 4 end style

Dengan demikian, nilai dari begin mathsize 14px style f apostrophe left parenthesis 0 right parenthesis end style adalah begin mathsize 14px style 11 over 4 end style.

Jadi, jawaban yang tepat adalah A.

0

Roboguru

Turunan pertama dari f(x)=5x+2x2−3​ adalah  f(x). Nilai f(0)=...

Pembahasan Soal:

Bentuk fungsi,

f left parenthesis x right parenthesis equals fraction numerator u left parenthesis x right parenthesis over denominator v left parenthesis x right parenthesis space end fraction

Memiliki turunan pertama yang berbentuk

f apostrophe left parenthesis x right parenthesis equals fraction numerator u to the power of apostrophe left parenthesis x right parenthesis v left parenthesis x right parenthesis minus v to the power of apostrophe left parenthesis x right parenthesis u left parenthesis x right parenthesis over denominator v squared left parenthesis x right parenthesis end fraction

Jika

f left parenthesis x right parenthesis equals fraction numerator x squared minus 3 over denominator 5 x plus 2 end fraction maka :

u left parenthesis x right parenthesis equals x squared minus 3 rightwards arrow u to the power of apostrophe left parenthesis x right parenthesis equals 2 x  v left parenthesis x right parenthesis equals 5 x plus 2 rightwards arrow v to the power of apostrophe left parenthesis x right parenthesis equals 5

Maka

f to the power of apostrophe left parenthesis x right parenthesis equals fraction numerator 2 x left parenthesis 5 x plus 2 right parenthesis minus 5 left parenthesis x squared minus 3 right parenthesis over denominator left parenthesis 5 x plus 2 right parenthesis squared end fraction  f to the power of apostrophe left parenthesis 0 right parenthesis equals fraction numerator 2 left parenthesis 0 right parenthesis left parenthesis 5 left parenthesis 0 right parenthesis plus 2 right parenthesis minus 5 left parenthesis 0 minus 3 right parenthesis over denominator left parenthesis 5 left parenthesis 0 right parenthesis plus 2 right parenthesis squared end fraction  f to the power of apostrophe left parenthesis 0 right parenthesis equals fraction numerator 15 over denominator left parenthesis 2 right parenthesis squared end fraction  f to the power of apostrophe left parenthesis 0 right parenthesis equals 15 over 4

0

Roboguru

Tentukan turunan fungsi-fungsi berikut. f(x)=(x2+5)(x2+2x−3)​

Pembahasan Soal:

Sifat: Jika begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator u open parentheses x close parentheses over denominator v open parentheses x close parentheses end fraction end style, maka begin mathsize 14px style f apostrophe open parentheses x close parentheses equals fraction numerator u apostrophe open parentheses x close parentheses times v open parentheses x close parentheses minus u open parentheses x close parentheses times v apostrophe open parentheses x close parentheses over denominator v squared open parentheses x close parentheses end fraction end style

Turunan fungsi dari begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator open parentheses x squared plus 2 x minus 3 close parentheses over denominator open parentheses x squared plus 5 close parentheses end fraction end style adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator open parentheses 2 x plus 2 close parentheses open parentheses x squared plus 5 close parentheses minus open parentheses x squared plus 2 x minus 3 close parentheses open parentheses 2 x close parentheses over denominator open parentheses x squared plus 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 x cubed plus 2 x squared plus 10 x plus 10 minus open parentheses 2 x cubed plus 4 x squared minus 6 x close parentheses over denominator open parentheses x squared plus 5 close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 2 x squared plus 16 x plus 10 over denominator open parentheses x squared plus 5 close parentheses squared end fraction end cell end table end style

Dengan demikian, turunan fungsi tersebut adalah begin mathsize 14px style f apostrophe open parentheses x close parentheses equals fraction numerator negative 2 x squared plus 16 x plus 10 over denominator open parentheses x squared plus 5 close parentheses squared end fraction end style 

0

Roboguru

Tentukan turunan pertama dari setiap fungsi berikut: 3. f(x)=2x+33x−1​ dengan x=−23​

Pembahasan Soal:

Ingat kembali turunan fungsi aljabar 

table attributes columnalign right center left columnspacing 0px end attributes row cell a open parentheses x close parentheses end cell equals cell x to the power of n plus x to the power of n minus 1 end exponent plus horizontal ellipsis plus x end cell row cell fraction numerator straight d a open parentheses x close parentheses over denominator d x end fraction end cell equals cell n x to the power of open parentheses n minus 1 close parentheses end exponent plus open parentheses n minus 1 close parentheses x to the power of open parentheses n minus 2 close parentheses end exponent plus horizontal ellipsis plus 1 end cell end table 

dan aturan turunan pada perkalian dua fungsi

table attributes columnalign right center left columnspacing 0px end attributes row cell a open parentheses x close parentheses end cell equals cell fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction end cell row cell a apostrophe open parentheses x close parentheses end cell equals cell fraction numerator f apostrophe open parentheses x close parentheses g open parentheses x close parentheses minus g apostrophe open parentheses x close parentheses f open parentheses x close parentheses over denominator g open parentheses x close parentheses squared end fraction end cell end table

sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 3 x minus 1 over denominator 2 x plus 3 end fraction end cell row cell f apostrophe open parentheses x close parentheses end cell equals cell fraction numerator 3 open parentheses 2 x plus 3 close parentheses minus 2 open parentheses 3 x minus 1 close parentheses over denominator open parentheses 2 x plus 3 close parentheses squared end fraction end cell row blank equals cell fraction numerator 6 x plus 9 minus 6 x plus 2 over denominator open parentheses 2 x plus 3 close parentheses squared end fraction end cell row blank equals cell 11 over open parentheses 2 x plus 3 close parentheses squared end cell end table 

Jadi, turunan pertama dari f open parentheses x close parentheses equals fraction numerator 3 x minus 1 over denominator 2 x plus 3 end fraction adalah 11 over open parentheses 2 x plus 3 close parentheses squared.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved