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Aula: Determinando Derivadas de Funções Polinomiais

Nesta aula, nós vamos aprender como determinar derivadas de funções polinomiais.

Atividade • 24 Questões

Q1:

Dados que ๐‘ฆ = ๐‘ฅ + ๐‘ฅ + 8 ๐‘ฅ 3 2 e ๐‘ง = ๐‘ฅ ( ๐‘ฅ โˆ’ 4 ) ( ๐‘ฅ โˆ’ 1 ) , determine d d d d ๐‘ฆ ๐‘ฅ โˆ’ ๐‘ง ๐‘ฅ .

  • A 1 2 ๐‘ฅ + 4
  • B โˆ’ 8 ๐‘ฅ + 4
  • C 1 2 ๐‘ฅ + 1 2
  • D โˆ’ 2 ๐‘ฅ โˆ’ 4
  • E โˆ’ 4 ๐‘ฅ โˆ’ 4

Q2:

Determine d d ๐‘ฆ ๐‘ฅ , sendo โˆ’ 6 ๐‘ฅ ๐‘ฆ = 1 1 .

  • A 1 1 6 ๐‘ฅ ๏Šจ
  • B โˆ’ 1 1 ๐‘ฆ 6 ๐‘ฅ
  • C 1 1 โˆ’ 6 ๐‘ฆ ๐‘ฅ ๐‘ฅ
  • D 1 1 6 ๐‘ฅ

Q3:

Sendo ๐‘ฆ = 1 5 โˆ’ 1 ๐‘ฅ + 1 3 ๐‘ฅ ๏Šฌ ๏Šจ ๏Šฆ , determine ๐‘ฆ โ€ฒ .

  • A 6 ๐‘ฅ + 2 0 3 ๐‘ฅ ๏Šญ ๏Šง ๏Šฏ
  • B 6 ๐‘ฅ + 2 0 3 ๐‘ฅ ๏Šฌ ๏Šจ ๏Šฆ
  • C 5 ๐‘ฅ + 1 9 3 ๐‘ฅ ๏Šญ ๏Šง ๏Šฏ
  • D 1 ๐‘ฅ + 1 3 ๐‘ฅ ๏Šญ ๏Šง ๏Šฏ

Q4:

Determine d d ๐‘ฆ ๐‘ฅ , sabendo que ๐‘ฆ = 7 ๐‘ฅ + 1 ๐‘ฅ ๏Šซ ๏Šฌ .

  • A 3 5 ๐‘ฅ โˆ’ 6 ๐‘ฅ ๏Šช ๏Šญ
  • B 3 5 ๐‘ฅ + 6 ๐‘ฅ ๏Šซ ๏Šฌ
  • C 3 5 ๐‘ฅ โˆ’ 6 ๐‘ฅ ๏Šซ ๏Šฌ
  • D 3 5 ๐‘ฅ โˆ’ 6 ๐‘ฅ ๏Šฌ ๏Šญ
  • E 7 ๐‘ฅ + 1 ๐‘ฅ ๏Šช ๏Šซ

Q5:

Determine a primeira derivada da funรงรฃo ๐‘ฆ = 2 ๐‘ฅ ๏€น 9 ๐‘ฅ โˆ’ 3 ๐‘ฅ ๏… + 1 0 ๐‘ฅ 2 .

  • A 5 4 ๐‘ฅ โˆ’ 1 2 ๐‘ฅ + 1 0 2
  • B 1 8 ๐‘ฅ โˆ’ 6 ๐‘ฅ + 1 0 2
  • C 1 8 ๐‘ฅ โˆ’ 6 ๐‘ฅ + 1 0 ๐‘ฅ 4 3 2
  • D 5 4 ๐‘ฅ โˆ’ 1 2 ๐‘ฅ + 1 0 ๐‘ฅ 4 3 2

Q6:

Dado que ๐‘ฆ = ( ๐‘ฅ โˆ’ 1 1 ) 3 , determine ๏€ฝ ๐‘ฆ ๐‘ฅ ๏‰ โˆ’ ๐‘ฆ ( ๐‘ฅ โˆ’ 1 1 ) ๐‘ฆ ๐‘ฅ d d d d 3 .

  • A 2 4 ๐‘ฆ 2
  • B 9 0 ๐‘ฆ 2
  • C ( ๐‘ฅ โˆ’ 1 1 ) โˆ’ ( ๐‘ฅ โˆ’ 1 1 ) 3 0 8
  • D ( ๐‘ฅ โˆ’ 1 1 ) โˆ’ ( ๐‘ฅ โˆ’ 1 1 ) 2 4 6

Q7:

Calcule d d ๐‘ฅ ๏€พ โˆš 3 ๐‘ฅ + ๐‘ฅ 9 + 6 ๐œ‹ ๏Š 7 9 .

  • A 7 โˆš 3 ๐‘ฅ + ๐‘ฅ 6 8
  • B 7 โˆš 3 ๐‘ฅ + 8 ๐‘ฅ 6 8
  • C โˆš 3 7 ๐‘ฅ + ๐‘ฅ 8 1 6 8
  • D 7 โˆš 3 ๐‘ฅ + 8 9 ๐‘ฅ 6 8
  • E 7 โˆš 3 ๐‘ฅ + ๐‘ฅ + 6 6 8

Q8:

Resolva ๐‘“ โ€ฒ ( ๐‘ฅ ) = 8 1 para ๐‘ฅ , onde ๐‘“ ( ๐‘ฅ ) = ( 9 ๐‘ฅ + 1 ) 9 .

  • A ๐‘ฅ = 0 โˆ’ 2 9 o u
  • B ๐‘ฅ = 2 9 0 o u
  • C ๐‘ฅ = 1 0 8 o u
  • D ๐‘ฅ = โˆ’ 8 โˆ’ 1 0 o u

Q9:

Encontre a primeira derivada da funรงรฃo ๐‘“ ( ๐‘ฅ ) = โˆ’ 2 ๐‘ฅ + 1 0 .

Q10:

Determine d d ๐‘ฆ ๐‘ฅ , sendo ๐‘ฆ = ( 7 ๐‘ฅ + 3 ) 4 .

  • A 2 8 ( 7 ๐‘ฅ + 3 ) 3
  • B 2 1 ( 7 ๐‘ฅ + 3 ) 3
  • C 2 8 ( 7 ๐‘ฅ + 3 ) 5
  • D 4 ( 7 ๐‘ฅ + 3 ) 3

Q11:

Dado que ๐‘ฆ = 3 ๐‘ฅ ๐‘’ ๏Šญ ๏Šฑ ๏Šฌ , determine d d ๐‘ฆ ๐‘ฅ .

  • A 2 1 ๐‘ฅ ๐‘’ ๏Šฌ ๏Šฑ ๏Šฌ
  • B 3 ๐‘ฅ ๐‘’ ๏Šฌ ๏Šฑ ๏Šฌ
  • C โˆ’ 1 8 ๐‘ฅ ๐‘’ + 3 ๐‘ฅ ๐‘’ ๏Šญ ๏Šฌ ๏Šฌ ๏Šฌ
  • D โˆ’ 1 8 ๐‘ฅ ๐‘’ + 2 1 ๐‘ฅ ๐‘’ ๏Šญ ๏Šฌ ๏Šฌ ๏Šฌ

Q12:

Encontre a primeira derivada da funรงรฃo ๐‘ฆ = ๐‘ฅ โˆ’ ๐‘ฅ 4 โˆ’ 3 ๐‘ฅ + 6 ๏Šช ๏Šฉ .

  • A 4 ๐‘ฅ โˆ’ 3 ๐‘ฅ 4 โˆ’ 3 ๏Šฉ ๏Šจ
  • B 3 ๐‘ฅ โˆ’ ๐‘ฅ 2 โˆ’ 3 ๏Šฉ ๏Šจ
  • C 4 ๐‘ฅ โˆ’ 3 ๐‘ฅ 4 โˆ’ 3 ๐‘ฅ + 6 ๐‘ฅ ๏Šซ ๏Šช ๏Šจ
  • D ๐‘ฅ โˆ’ ๐‘ฅ 4 โˆ’ 3 ๏Šฉ ๏Šจ

Q13:

Determine a primeira derivada da funรงรฃo ๐‘“ ( ๐‘ฅ ) = ๏€น ๐‘ฅ + 8 ๏… ๏€น 3 ๐‘ฅ โˆ’ 8 ๐‘ฅ + 6 ๏… ๏Šจ ๏Šฉ .

  • A 1 5 ๐‘ฅ + 4 8 ๐‘ฅ + 1 2 ๐‘ฅ โˆ’ 6 4 ๏Šช ๏Šจ
  • B 1 2 ๐‘ฅ + 3 2 ๐‘ฅ + 6 ๐‘ฅ โˆ’ 6 4 ๏Šช ๏Šจ
  • C 1 8 ๐‘ฅ + 4 8 ๐‘ฅ + 1 2 ๐‘ฅ โˆ’ 6 4 ๏Šซ ๏Šจ
  • D 3 ๐‘ฅ + 1 6 ๐‘ฅ + 6 ๐‘ฅ โˆ’ 6 4 ๏Šช ๏Šจ

Q14:

Resolva ๐‘“ โ€ฒ ( ๐‘ฅ ) = โˆ’ 2 7 em ordem a ๐‘ฅ , sendo ๐‘“ ( ๐‘ฅ ) = ( โˆ’ 9 ๐‘ฅ โˆ’ 4 ) 3 .

  • A ๐‘ฅ = โˆ’ 1 3 , ๐‘ฅ = โˆ’ 5 9
  • B ๐‘ฅ = โˆ’ 1 3
  • C ๐‘ฅ = 5 9 , ๐‘ฅ = โˆ’ 5 9
  • D ๐‘ฅ = โˆ’ 5 9
  • E ๐‘ฅ = โˆ’ 1 3 , ๐‘ฅ = 1 3

Q15:

Determine d d ๐‘ฆ ๐‘ฅ , sabendo que ๐‘ฆ = โˆ’ 8 ๐‘ฅ โˆ’ 4 ๐‘ฅ + 3 ๐‘ฅ + 5 9 5 .

  • A โˆ’ 7 2 ๐‘ฅ โˆ’ 2 0 ๐‘ฅ + 3 8 4
  • B โˆ’ 7 2 ๐‘ฅ โˆ’ 2 0 ๐‘ฅ 1 0 6
  • C โˆ’ 8 ๐‘ฅ โˆ’ 4 ๐‘ฅ + 3 8 4
  • D โˆ’ 7 2 ๐‘ฅ โˆ’ 2 0 ๐‘ฅ + 3 9 5

Q16:

Dado que ๐‘ฆ = ( ๐‘˜ โˆ’ 5 ๐‘ฅ ) ๏Šฉ , e d d ๐‘ฆ ๐‘ฅ = โˆ’ 1 5 em ๐‘ฅ = โˆ’ 2 , encontre os valores de ๐‘˜ .

  • A โˆ’ 9 , โˆ’ 1 1
  • B15, 5
  • C โˆ’ 1 0 , โˆ’ 1 2
  • D โˆ’ 1 5 , 2

Q17:

Suponha ๐‘“ ( ๐‘ฅ ) = ( โˆ’ 2 ๐‘ฅ + ๐‘Ž ) ๏€น 3 ๐‘ฅ โˆ’ ๐‘Ž ๏… ๏Šจ e ๐‘“ โ€ฒ ( โˆ’ 1 ) = โˆ’ 1 0 . Determine ๐‘Ž .

Q18:

Calcule d d ๐‘ฅ ๏€น โˆ’ 3 ๐‘ฅ โˆ’ 4 ๐‘ฅ + 5 ๏… 2 .

  • A โˆ’ 6 ๐‘ฅ โˆ’ 4
  • B โˆ’ 3 ๐‘ฅ โˆ’ 4
  • C โˆ’ 9 ๐‘ฅ โˆ’ 4 ๐‘ฅ 3
  • D โˆ’ 9 ๐‘ฅ โˆ’ 4 3

Q19:

Dado que ๐‘“ ( ๐‘ฅ ) = โˆ’ ๐‘ฅ + ๐‘š ๐‘ฅ + 1 ๏Šจ , determine ๐‘š se ๐‘“ โ€ฒ ( 3 ) = 1 .

Q20:

Diferencie ๐‘“ ( ๐‘ฅ ) = 1 2 ๐‘ฅ โˆ’ 1 5 ๐‘ฅ + 1 8 ๐‘ฅ ๏Šง ๏Šฎ ๏Šจ ๏Šซ ๏Šฉ ๏Šจ .

  • A 9 ๐‘ฅ โˆ’ 5 ๐‘ฅ + 4 ๐‘ฅ ๏Šง ๏Šญ ๏Šจ ๏Šช ๏Šฉ ๏Šง
  • B 1 2 ๐‘ฅ โˆ’ 1 5 ๐‘ฅ + 1 8 ๐‘ฅ ๏Šง ๏Šญ ๏Šจ ๏Šช ๏Šฉ ๏Šง
  • C 1 2 ๐‘ฅ โˆ’ 1 5 ๐‘ฅ + 1 8 ๐‘ฅ ๏Šง ๏Šฏ ๏Šจ ๏Šฌ ๏Šฉ ๏Šฉ
  • D 9 ๐‘ฅ โˆ’ 5 ๐‘ฅ + 4 ๐‘ฅ ๏Šง ๏Šฏ ๏Šจ ๏Šฌ ๏Šฉ ๏Šฉ

Q21:

Derive ๐‘“ ( ๐‘ฅ ) = 8 ๐‘ฅ โˆ’ 7 ๐‘ฅ โˆ’ 2 ๏Šจ .

  • A 1 6 ๐‘ฅ โˆ’ 7
  • B 8 ๐‘ฅ โˆ’ 7
  • C 8 ๐‘ฅ โˆ’ 7 ๐‘ฅ โˆ’ 2 ๐‘ฅ ๏Šฉ ๏Šจ
  • D 1 6 ๐‘ฅ โˆ’ 7 ๐‘ฅ โˆ’ 2 ๐‘ฅ ๏Šฉ ๏Šจ

Q22:

Encontre a primeira derivada da funรงรฃo ๐‘ฆ = ( 4 โˆ’ 5 ๐‘ฅ ) ๏Šช .

  • A โˆ’ 2 0 ( 4 โˆ’ 5 ๐‘ฅ ) ๏Šฉ
  • B 4 ( 4 โˆ’ 5 ๐‘ฅ ) ๏Šฉ
  • C 4 ( 4 โˆ’ 5 ๐‘ฅ ) ๏Šซ
  • D โˆ’ 2 0 ( 4 โˆ’ 5 ๐‘ฅ ) ๏Šซ

Q23:

Encontre d d ๐‘ฆ ๐‘ฅ se ๐‘ฆ = 2 ๐‘ฅ ๏Šฑ ๏Šญ .

  • A โˆ’ 1 4 ๐‘ฅ ๏Šฑ ๏Šฎ
  • B โˆ’ 1 4 ๐‘ฅ ๏Šฑ ๏Šฌ
  • C โˆ’ 1 6 ๐‘ฅ ๏Šฑ ๏Šฎ
  • D 2 ๐‘ฅ ๏Šฑ ๏Šฎ

Q24:

Dado que ๐‘ฆ = โˆ’ 2 5 ๐‘ฅ , determine d d ๐‘ฆ ๐‘ฅ .
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