Diketahui y=2x3+4x2+16x+21, tentukan turunan pertama dari y menggunakan cara limit!

Pertanyaan

Diketahui y equals 2 x cubed plus 4 x squared plus 16 x plus 21, tentukan turunan pertama dari y menggunakan cara limit!

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

Diketahui y equals 2 x cubed plus 4 x squared plus 16 x plus 21. Ingat bahwa 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d y over denominator d x end fraction end cell equals cell stack l i m with h rightwards arrow 0 below fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction end cell end table

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 2 x cubed plus 4 x squared plus 16 x plus 21 end cell row cell f left parenthesis x plus h right parenthesis end cell equals cell 2 left parenthesis x plus h right parenthesis cubed plus 4 left parenthesis x plus h right parenthesis squared plus 16 left parenthesis x plus h right parenthesis plus 21 end cell row cell f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis end cell equals cell 2 h cubed plus 6 x h squared plus 6 x squared h plus 4 h squared plus 8 x h plus 16 h end cell row cell fraction numerator d y over denominator d x end fraction end cell equals cell stack l i m with h rightwards arrow 0 below fraction numerator f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis over denominator h end fraction end cell row blank equals cell stack l i m with h rightwards arrow 0 below fraction numerator 2 h cubed plus 6 x h squared plus 6 x squared h plus 4 h squared plus 8 x h plus 16 h over denominator h end fraction end cell row blank equals cell stack l i m with h rightwards arrow 0 below 2 h squared plus 6 x h plus 6 x squared plus 4 h plus 8 x plus 16 end cell row blank equals cell 6 x squared plus 8 x plus 16 end cell end table

Oleh karena itu, turunan pertama dari y equals 2 x cubed plus 4 x squared plus 16 x plus 21 adalah 6 x squared plus 8 x plus 16.

 

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