Pertanyaan

Jika f ( x ) = x 3 + 3 x 2 + 4 x + 5 x 2 + 4 x + 5 , tentukan nilai dari f ( x ) ?

Jika $f (x) = \frac{x ^{2} + 4 x + 5}{x ^{3} + 3 x ^{2} + 4 x + 5}$ , tentukan nilai dari $f (x)$ ?

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

Diketahui. Ingat bahwa maka Oleh karena itu, turunan pertama dari adalah .

Diketahui . Ingat bahwa

$table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell u over v rightwards arrow f apostrophe left parenthesis x right parenthesis equals fraction numerator u apostrophe v minus u v apostrophe over denominator v squared end fraction end cell end table$

maka

$table attributes columnalign right center left columnspacing 0px end attributes row U equals cell x squared plus 4 x plus 5 end cell row cell U apostrophe end cell equals cell 2 x plus 4 end cell row V equals cell x cubed plus 3 x squared plus 4 x plus 5 end cell row cell V apostrophe end cell equals cell 3 x squared plus 6 x plus 4 end cell row cell U apostrophe V end cell equals cell 2 x to the power of 4 plus 10 x cubed plus 20 x squared plus 26 x plus 20 end cell row cell U V apostrophe end cell equals cell 3 x to the power of 4 plus 18 x cubed plus 43 x squared plus 46 x plus 20 end cell row cell U apostrophe V minus U V apostrophe end cell equals cell negative x to the power of 4 minus 8 x cubed minus 23 x squared minus 20 x end cell row cell V squared end cell equals cell x to the power of 6 plus 6 x to the power of 5 plus 17 x to the power of 4 plus 34 x cubed plus 46 x squared plus 40 x plus 25 end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator U apostrophe V minus U V apostrophe over denominator V squared end fraction end cell row blank equals cell fraction numerator negative x to the power of 4 minus 8 x cubed minus 23 x squared minus 20 x over denominator x to the power of 6 plus 6 x to the power of 5 plus 17 x to the power of 4 plus 34 x cubed plus 46 x squared plus 40 x plus 25 end fraction end cell end table$

Oleh karena itu, turunan pertama dari $f left parenthesis x right parenthesis equals fraction numerator x squared plus 4 x plus 5 over denominator x cubed plus 3 x squared plus 4 x plus 5 end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row cell f apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator negative x to the power of 4 minus 8 x cubed minus 23 x squared minus 20 x over denominator x to the power of 6 plus 6 x to the power of 5 plus 17 x to the power of 4 plus 34 x cubed plus 46 x squared plus 40 x plus 25 end fraction end cell end table$ .