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Jika f (x) adalah turunan pertama fungsi f(x)=(2x−3)4(−x+8)5, rumus  adalah ...

Pertanyaan

Jika f apostrophe open parentheses x close parentheses adalah turunan pertama fungsi f left parenthesis x right parenthesis equals open parentheses 2 x minus 3 close parentheses to the power of 4 open parentheses negative x plus 8 close parentheses to the power of 5, rumus f apostrophe open parentheses x close parentheses adalah ...

R. Azizatul

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta

Jawaban terverifikasi

Jawaban

turunan pertama dari f left parenthesis x right parenthesis equals open parentheses 2 x minus 3 close parentheses to the power of 4 open parentheses negative x plus 8 close parentheses to the power of 5 adalah f apostrophe open parentheses x close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 2 x minus 3 right parenthesis cubed left parenthesis negative x plus 8 right parenthesis to the power of 4 left parenthesis negative 18 x plus 79 right parenthesis end cell end table.

Pembahasan

Ingat

  • aturan rantai  y equals open parentheses a x plus b close parentheses to the power of n rightwards arrow y apostrophe equals n open parentheses a x plus b close parentheses to the power of n minus 1 end exponent times a 
  • sifat turunan pada perkalian fungsi begin mathsize 14px style y equals u times v rightwards arrow y apostrophe equals u apostrophe times v plus u times v apostrophe end style

Maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell left parenthesis 2 x minus 3 right parenthesis to the power of 4 left parenthesis negative x plus 8 right parenthesis to the power of 5 space space end cell row cell f apostrophe left parenthesis x right parenthesis end cell equals cell 4 left parenthesis 2 x minus 3 right parenthesis cubed left parenthesis 2 right parenthesis left parenthesis negative x plus 8 right parenthesis to the power of 5 plus left parenthesis 2 x minus 3 right parenthesis to the power of 4 5 left parenthesis negative x plus 8 right parenthesis to the power of 4 left parenthesis negative 1 right parenthesis end cell row blank equals cell 8 left parenthesis 2 x minus 3 right parenthesis cubed left parenthesis negative x plus 8 right parenthesis to the power of 5 minus 5 left parenthesis 2 x minus 3 right parenthesis to the power of 4 left parenthesis negative x plus 8 right parenthesis to the power of 4 end cell row blank equals cell left parenthesis 2 x minus 3 right parenthesis cubed left parenthesis negative x plus 8 right parenthesis to the power of 4 left parenthesis 8 left parenthesis negative x plus 8 right parenthesis minus 5 left parenthesis 2 x minus 3 right parenthesis right parenthesis end cell row blank equals cell left parenthesis 2 x minus 3 right parenthesis cubed left parenthesis negative x plus 8 right parenthesis to the power of 4 left parenthesis negative 8 x plus 64 minus 10 x plus 15 right parenthesis end cell row blank equals cell left parenthesis 2 x minus 3 right parenthesis cubed left parenthesis negative x plus 8 right parenthesis to the power of 4 left parenthesis negative 18 x plus 79 right parenthesis end cell end table end style 

Dengan demikian, turunan pertama dari f left parenthesis x right parenthesis equals open parentheses 2 x minus 3 close parentheses to the power of 4 open parentheses negative x plus 8 close parentheses to the power of 5 adalah f apostrophe open parentheses x close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 2 x minus 3 right parenthesis cubed left parenthesis negative x plus 8 right parenthesis to the power of 4 left parenthesis negative 18 x plus 79 right parenthesis end cell end table.

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