Atividade: Derivadas de Funções Polinomiais

Nesta atividade, nós vamos praticar a calcular derivadas de funções polinomiais.

Q1:

Derive a funรงรฃo ๐‘“ ( ๐‘ฅ ) = โˆ’ ๐‘ฅ 7 โˆ’ 3 ๐‘ฅ โˆ’ 4 ๏Šจ .

  • A ๐‘“ ( ๐‘ฅ ) = โˆ’ 2 ๐‘ฅ 7 โˆ’ 3 ๐‘ฅ โˆ’ 4 ๐‘ฅ ๏Ž˜ ๏Šฉ ๏Šจ
  • B ๐‘“ ( ๐‘ฅ ) = โˆ’ ๐‘ฅ 7 โˆ’ 3 ๏Ž˜
  • C ๐‘“ ( ๐‘ฅ ) = โˆ’ ๐‘ฅ 7 โˆ’ 3 ๐‘ฅ โˆ’ 4 ๐‘ฅ ๏Ž˜ ๏Šฉ ๏Šจ
  • D ๐‘“ ( ๐‘ฅ ) = โˆ’ 2 ๐‘ฅ 7 โˆ’ 3 ๏Ž˜
  • E ๐‘“ ( ๐‘ฅ ) = โˆ’ 2 ๐‘ฅ 7 โˆ’ 3 ๐‘ฅ โˆ’ 4 ๏Ž˜ ๏Šจ

Q2:

Dados que ๐‘ฆ = ๐‘ฅ + ๐‘ฅ + 8 ๐‘ฅ ๏Šฉ ๏Šจ 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 โˆ’ 4 ๐‘ฅ โˆ’ 4
  • B 1 2 ๐‘ฅ + 1 2
  • C โˆ’ 2 ๐‘ฅ โˆ’ 4
  • D 1 2 ๐‘ฅ + 4
  • E โˆ’ 8 ๐‘ฅ + 4

Q3:

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

  • A 1 1 6 ๐‘ฅ
  • 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 ๏Šจ

Q4:

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

  • A 1 ๐‘ฅ + 1 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 6 ๐‘ฅ + 2 0 3 ๐‘ฅ ๏Šญ ๏Šง ๏Šฏ

Q5:

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

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

Q6:

Encontre d d ๐‘ฆ ๐‘ฅ , dado que ๐‘ฆ = 2 2 ๐‘ฅ ๏Šช .

  • A 8 8 ๐‘ฅ ๏Šซ
  • B 8 8 ๐‘ฅ ๏Šช
  • C 2 2 ๐‘ฅ ๏Šซ
  • D 8 8 ๐‘ฅ ๏Šฉ

Q7:

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

  • A 5 4 ๐‘ฅ โˆ’ 1 2 ๐‘ฅ + 1 0 ๐‘ฅ ๏Šช ๏Šฉ ๏Šจ
  • B 1 8 ๐‘ฅ โˆ’ 6 ๐‘ฅ + 1 0 ๏Šจ
  • C 1 8 ๐‘ฅ โˆ’ 6 ๐‘ฅ + 1 0 ๐‘ฅ ๏Šช ๏Šฉ ๏Šจ
  • D 5 4 ๐‘ฅ โˆ’ 1 2 ๐‘ฅ + 1 0 ๏Šจ

Q8:

Calcule ๐‘“ โ€ฒ ( 3 ) , onde ๐‘“ ( ๐‘ฅ ) = 1 7 ๐‘ฅ + 5 2 ๐‘ฅ ๏Šจ .

Q9:

Derive a funรงรฃo ๐‘“ ( ๐‘ก ) = 6 , 3 ๐‘ก + 5 , 2 ๐‘ก + 7 , 3 ๏Šซ ๏Šจ .

  • A ๐‘“ ( ๐‘ก ) = 6 , 3 ๐‘ก + 5 , 2 ๐‘ก + 7 , 3 ๐‘ก ๏Ž˜ ๏Šฌ ๏Šฉ
  • B ๐‘“ ( ๐‘ก ) = 6 , 3 ๐‘ก + 5 , 2 ๐‘ก ๏Ž˜ ๏Šช
  • C ๐‘“ ( ๐‘ก ) = 3 1 , 5 ๐‘ก + 1 0 , 4 ๐‘ก + 7 , 3 ๐‘ก ๏Ž˜ ๏Šฌ ๏Šฉ
  • D ๐‘“ ( ๐‘ก ) = 3 1 , 5 ๐‘ก + 1 0 , 4 ๐‘ก ๏Ž˜ ๏Šช
  • E ๐‘“ ( ๐‘ก ) = 2 5 , 2 ๐‘ก + 5 , 2 ๐‘ก ๏Ž˜ ๏Šช

Q10:

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

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

Q11:

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

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

Q12:

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

Q13:

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

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

Q14:

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

Q15:

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

  • A ๐‘ฅ โˆ’ 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 4 ๐‘ฅ โˆ’ 3 ๐‘ฅ 4 โˆ’ 3 ๏Šฉ ๏Šจ

Q16:

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 3 ๐‘ฅ + 1 6 ๐‘ฅ + 6 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 1 5 ๐‘ฅ + 4 8 ๐‘ฅ + 1 2 ๐‘ฅ โˆ’ 6 4 ๏Šช ๏Šจ

Q17:

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

  • A โˆ’ 7 2 ๐‘ฅ โˆ’ 2 0 ๐‘ฅ + 3 ๏Šฏ ๏Šซ
  • B โˆ’ 7 2 ๐‘ฅ โˆ’ 2 0 ๐‘ฅ ๏Šง ๏Šฆ ๏Šฌ
  • C โˆ’ 8 ๐‘ฅ โˆ’ 4 ๐‘ฅ + 3 ๏Šฎ ๏Šช
  • D โˆ’ 7 2 ๐‘ฅ โˆ’ 2 0 ๐‘ฅ + 3 ๏Šฎ ๏Šช

Q18:

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

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

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:

Se a funรงรฃo ๐‘“ ( ๐‘ฅ ) = โˆ’ 3 ๐‘ฅ โˆ’ 5 9 , determine l i m โ„Ž โ†’ 0 ๐‘“ ( ๐‘ฅ + โ„Ž ) โˆ’ ๐‘“ ( ๐‘ฅ ) โ„Ž .

  • A โˆ’ 2 7
  • B โˆ’ 2 7 ๐‘ฅ 9
  • C โˆ’ 3 ๐‘ฅ 9
  • D โˆ’ 2 7 ๐‘ฅ 8
  • E โˆ’ 2 7 ๐‘ฅ โˆ’ 5 โ„Ž 8

Q21:

Determine d d ๐‘ฆ ๐‘ฅ se ๐‘ฆ = 6 โˆš ๐‘ฅ 7 .

  • A 6 7 โˆš ๐‘ฅ
  • B 3 โˆš ๐‘ฅ 7
  • C โˆ’ 3 7 โˆš ๐‘ฅ
  • D 3 7 โˆš ๐‘ฅ

Q22:

Se ๐‘ฆ = 5 ( 2 ๐‘ฅ + 2 ๐‘ฅ ) c o s s e n 2 2 , determine d d ๐‘ฆ ๐‘ฅ .

Q23:

Se ๐‘ฆ = 1 5 8 ๐‘ฅ โˆ’ 1 5 8 ๐‘ฅ s e n c o s 2 2 , determine d d ๐‘ฆ ๐‘ฅ .

  • A 1 5 1 6 ๐‘ฅ s e n
  • B โˆ’ 2 4 0 1 6 ๐‘ฅ s e n
  • C โˆ’ 1 5 1 6 ๐‘ฅ s e n
  • D 2 4 0 1 6 ๐‘ฅ s e n
  • E0

Q24:

Encontre d d ๐‘ฆ ๐‘ฅ , dado que ๐‘ฆ = โˆ’ 4 3 ๐‘ฅ 8 .

  • A โˆ’ 3 4 4 ๐‘ฅ 8
  • B โˆ’ 3 4 4 ๐‘ฅ 7
  • C โˆ’ 4 3 ๐‘ฅ 7
  • D 3 4 4 ๐‘ฅ 9

Q25:

Encontre d d ๐‘ฆ ๐‘ฅ , dado que ๐‘ฆ = 3 ๐‘ฅ + 4 ๐‘ฅ + 6 โˆ’ 7 ๐‘ฅ โˆ’ 8 ๐‘ฅ ๏Šช ๏Šจ ๏Šญ ๏Šฎ .

  • A 1 2 ๐‘ฅ + 8 ๐‘ฅ + 6 + 4 9 ๐‘ฅ + 6 4 ๐‘ฅ ๏Šฉ ๏Šฌ ๏Šญ
  • B 1 2 ๐‘ฅ + 8 ๐‘ฅ + 6 + 4 9 ๐‘ฅ + 6 4 ๐‘ฅ ๏Šฉ ๏Šฎ ๏Šฏ
  • C 3 ๐‘ฅ + 4 ๐‘ฅ + 7 ๐‘ฅ + 8 ๐‘ฅ ๏Šฉ ๏Šฎ ๏Šฏ
  • D 1 2 ๐‘ฅ + 8 ๐‘ฅ + 4 9 ๐‘ฅ + 6 4 ๐‘ฅ ๏Šฉ ๏Šฎ ๏Šฏ
  • E 9 ๐‘ฅ + 4 ๐‘ฅ + 5 6 ๐‘ฅ + 7 2 ๐‘ฅ ๏Šฉ ๏Šฎ ๏Šฏ

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