Jika f(x)=x3+3x2+4x+5x2+4x+5​, tentukan nilai dari f (x)?

Pertanyaan

Jika 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, tentukan nilai dari f apostrophe left parenthesis x right parenthesis?

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

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.

 

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