RoboguruRoboguru
SD

Turunkan masing - masing ekspresi berikut terhadap t. c.  t​3t​−4​

Pertanyaan

Turunkan masing - masing ekspresi berikut terhadap t.

c.  undefined

Y. Dwi

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui undefined. Ingat untuk f open parentheses x close parentheses equals u over v berlaku table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction end cell end table.

Dimisalkan sebagai berikut.

u equals 3 square root of t minus 4 u equals 3 t to the power of 1 half end exponent minus 4  v equals square root of t v equals t to the power of 1 half end exponent 

Ingat sifat turunan fungsi a x to the power of n equals n times a x to the power of n minus 1 end exponent, maka diperoleh sebagai berikut.

u apostrophe equals 1 half 3 t to the power of 1 half minus 1 end exponent u apostrophe equals 3 over 2 t to the power of negative 1 half end exponent  v apostrophe equals 1 half t to the power of 1 half minus 1 end exponent v apostrophe equals 1 half t to the power of negative 1 half end exponent 

Dengan demikian, nilai f apostrophe open parentheses t close parentheses dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis t right parenthesis end cell equals cell fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction end cell row blank equals cell fraction numerator open parentheses begin display style 3 over 2 end style t to the power of negative begin display style 1 half end style end exponent times t to the power of begin display style 1 half end style end exponent close parentheses minus open parentheses open parentheses 3 t to the power of 1 half end exponent minus 4 close parentheses times 1 half t to the power of negative 1 half end exponent close parentheses over denominator open parentheses square root of t close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses begin display style 3 over 2 end style t to the power of 0 close parentheses minus open parentheses begin display style 3 over 2 end style t to the power of 0 minus 2 t to the power of negative 1 half end exponent close parentheses over denominator t end fraction end cell row blank equals cell fraction numerator begin display style 3 over 2 end style minus begin display style 3 over 2 end style plus 2 t to the power of negative 1 half end exponent over denominator t end fraction end cell row blank equals cell fraction numerator 2 t to the power of negative 1 half end exponent over denominator t end fraction end cell row blank equals cell 2 t to the power of negative 1 half end exponent times t to the power of negative 1 end exponent end cell row blank equals cell 2 t to the power of negative 3 over 2 end exponent end cell row blank equals cell 2 over t to the power of begin display style 3 over 2 end style end exponent end cell row blank equals cell fraction numerator 2 over denominator t square root of t end fraction end cell row blank blank blank end table 

Dengan demikian, turunannya adalah fraction numerator 2 over denominator t square root of t end fraction.

 

43

0.0 (0 rating)

Pertanyaan serupa

Tentukan nilai limit berikut dengan dalil L'Hospital. x→1lim​3x+7​−2x​−1​

42

5.0

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