Pertanyaan

Turunan pertama dari fungsi f ( x ) = 2 x − 1 x , x  = 2 1 adalah ...

Turunan pertama dari fungsi $f (x) = \frac{x}{2 x - 1}, x \neq = \frac{1}{2}$ adalah ...

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

turunan pertama dari fungsi adalah .

turunan pertama dari fungsi $f left parenthesis x right parenthesis equals fraction numerator square root of x over denominator 2 x minus 1 end fraction comma space x not equal to 1 half$ adalah $fraction numerator square root of x open parentheses negative 2 x minus 1 close parentheses over denominator 8 x cubed minus 8 x squared plus 2 x end fraction$ .

Pembahasan

Mencari turunan: Jadi, turunan pertama dari fungsi adalah .

Mencari turunan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator square root of x over denominator 2 x minus 1 end fraction end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator straight d over denominator straight d x end fraction open parentheses f left parenthesis x right parenthesis close parentheses end cell row blank equals cell fraction numerator straight d over denominator straight d x end fraction open parentheses fraction numerator square root of x over denominator 2 x minus 1 end fraction close parentheses end cell row blank equals cell fraction numerator fraction numerator straight d over denominator straight d x end fraction open parentheses square root of x close parentheses open parentheses 2 x minus 1 close parentheses minus fraction numerator straight d over denominator straight d x end fraction open parentheses 2 x minus 1 close parentheses square root of x over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator fraction numerator straight d over denominator straight d x end fraction open parentheses x to the power of 1 half end exponent close parentheses open parentheses 2 x minus 1 close parentheses minus fraction numerator straight d over denominator straight d x end fraction open parentheses 2 x minus 1 close parentheses square root of x over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator fraction numerator 1 over denominator 2 square root of x end fraction open parentheses 2 x minus 1 close parentheses minus 2 square root of x over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator fraction numerator 2 x minus 1 over denominator 2 square root of x end fraction minus 2 square root of x over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator fraction numerator negative 2 x minus 1 over denominator 2 square root of x end fraction over denominator open parentheses 2 x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator negative 2 x minus 1 over denominator 2 square root of x open parentheses 2 x minus 1 close parentheses squared end fraction end cell row blank equals cell fraction numerator square root of x open parentheses negative 2 x minus 1 close parentheses over denominator 8 x cubed minus 8 x squared plus 2 x end fraction end cell end table$

Jadi, turunan pertama dari fungsi $f left parenthesis x right parenthesis equals fraction numerator square root of x over denominator 2 x minus 1 end fraction comma space x not equal to 1 half$ adalah $fraction numerator square root of x open parentheses negative 2 x minus 1 close parentheses over denominator 8 x cubed minus 8 x squared plus 2 x end fraction$ .