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Tentukan turunan pertama dari setiap fungsi berikut: 4. y=2x(10x−8)5

Pertanyaan

Tentukan turunan pertama dari setiap fungsi berikut:

4. y equals 2 x open parentheses 10 x minus 8 close parentheses to the power of 5

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

. turunan pertama dari y equals 2 x open parentheses 10 x minus 8 close parentheses to the power of 5 adalah y apostrophe equals open parentheses 10 x minus 8 close parentheses to the power of 4 open parentheses 120 x minus 16 close parentheses.

Pembahasan

Ingat kembali turunan fungsi aljabar 

table attributes columnalign right center left columnspacing 0px end attributes row cell a open parentheses x close parentheses end cell equals cell x to the power of n plus x to the power of n minus 1 end exponent plus horizontal ellipsis plus x end cell row cell fraction numerator straight d a open parentheses x close parentheses over denominator d x end fraction end cell equals cell n x to the power of open parentheses n minus 1 close parentheses end exponent plus open parentheses n minus 1 close parentheses x to the power of open parentheses n minus 2 close parentheses end exponent plus horizontal ellipsis plus 1 end cell end table 

aturan rantai

fraction numerator d f over denominator d x end fraction equals fraction numerator d f over denominator d u end fraction times fraction numerator d u over denominator d x end fraction

dan aturan turunan pada perkalian dua fungsi

table attributes columnalign right center left columnspacing 0px end attributes row cell a open parentheses x close parentheses end cell equals cell fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction end cell row cell a apostrophe open parentheses x close parentheses end cell equals cell fraction numerator f apostrophe open parentheses x close parentheses g open parentheses x close parentheses minus g apostrophe open parentheses x close parentheses f open parentheses x close parentheses over denominator g open parentheses x close parentheses squared end fraction end cell end table

sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 x open parentheses 10 x minus 8 close parentheses to the power of 5 end cell row cell y apostrophe end cell equals cell 2 open parentheses 10 x minus 8 close parentheses to the power of 5 plus 5 open parentheses 10 x minus 8 close parentheses to the power of 4 times 2 x times 10 end cell row cell y apostrophe end cell equals cell 2 open parentheses 10 x minus 8 close parentheses to the power of 5 plus 100 x open parentheses 10 x minus 8 close parentheses to the power of 4 end cell row cell y apostrophe end cell equals cell open parentheses 10 x minus 8 close parentheses to the power of 4 open parentheses 2 open parentheses 10 x minus 8 close parentheses plus 100 x close parentheses end cell row cell y apostrophe end cell equals cell open parentheses 10 x minus 8 close parentheses to the power of 4 open parentheses 20 x minus 16 plus 100 x close parentheses end cell row cell y apostrophe end cell equals cell open parentheses 10 x minus 8 close parentheses to the power of 4 open parentheses 120 x minus 16 close parentheses end cell end table

Jadi. turunan pertama dari y equals 2 x open parentheses 10 x minus 8 close parentheses to the power of 5 adalah y apostrophe equals open parentheses 10 x minus 8 close parentheses to the power of 4 open parentheses 120 x minus 16 close parentheses.

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