Pertanyaan

Turunan pertama fungsi adalah ...

Turunan pertama fungsi $f open parentheses x close parentheses equals blank fraction numerator x squared minus 4 over denominator square root of x end fraction$ adalah ...

8 dari 10 siswa nilainya naik

dengan paket belajar pilihan

Habis dalam

Klaim

M. Iqbal

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

turunan pertama fungsi adalah

turunan pertama fungsi $f open parentheses x close parentheses equals blank fraction numerator x squared minus 4 over denominator square root of x end fraction$ adalah f apostrophe open parentheses x close parentheses equals open parentheses 3 over 2 x to the power of 1 half end exponent minus 2 x to the power of negative 3 over 2 end exponent close parentheses

f apostrophe open parentheses x close parentheses equals open parentheses 3 over 2 x to the power of 1 half end exponent minus 2 x to the power of negative 3 over 2 end exponent close parentheses

Pembahasan

Ingat rumus turunan dan dimisalkan dan Sehingga diperoleh Jadi, turunan pertama fungsi adalah

Ingat rumus turunan $y equals u over v rightwards arrow y to the power of apostrophe equals fraction numerator u to the power of apostrophe times v minus u times v apostrophe over denominator v squared end fraction$ dan dimisalkan

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell x squared minus 4 end cell row cell u apostrophe end cell equals cell 2 x end cell end table

dan

Sehingga diperoleh

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

Jadi, turunan pertama fungsi $f open parentheses x close parentheses equals blank fraction numerator x squared minus 4 over denominator square root of x end fraction$ adalah f apostrophe open parentheses x close parentheses equals open parentheses 3 over 2 x to the power of 1 half end exponent minus 2 x to the power of negative 3 over 2 end exponent close parentheses