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‘ฅ7โˆ’3๐‘ฅโˆ’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 ๐‘ฅ โˆ’ 4 ๐‘ฅ ๏Ž˜ ๏Šฉ ๏Šจ
  • C ๐‘“ ( ๐‘ฅ ) = โˆ’ ๐‘ฅ 7 โˆ’ 3 ๏Ž˜
  • 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+8๐‘ฅ๏Šฉ๏Šจ e ๐‘ง=๐‘ฅ(๐‘ฅโˆ’4)(๐‘ฅโˆ’1), determine dddd๐‘ฆ๐‘ฅโˆ’๐‘ง๐‘ฅ.

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

Q3:

Determine dd๐‘ฆ๐‘ฅ, sendo โˆ’6๐‘ฅ๐‘ฆ=11.

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

Q4:

Sendo ๐‘ฆ=15โˆ’1๐‘ฅ+13๐‘ฅ๏Šฌ๏Šจ๏Šฆ, determine ๐‘ฆโ€ฒ.

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

Q5:

Determine dd๐‘ฆ๐‘ฅ, sabendo que ๐‘ฆ=7๐‘ฅ+1๐‘ฅ๏Šซ๏Šฌ.

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

Q6:

Encontre dd๐‘ฆ๐‘ฅ, dado que ๐‘ฆ=22๐‘ฅ๏Šช.

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

Q7:

Determine a primeira derivada da funรงรฃo ๐‘ฆ=2๐‘ฅ๏€น9๐‘ฅโˆ’3๐‘ฅ๏…+10๐‘ฅ๏Šจ.

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

Q8:

Calcule ๐‘“โ€ฒ(3), onde ๐‘“(๐‘ฅ)=17๐‘ฅ+52๐‘ฅ๏Šจ.

Q9:

Derive a funรงรฃo ๐‘“(๐‘ก)=6,3๐‘ก+5,2๐‘ก+7,3๏Šซ๏Šจ.

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

Q10:

Dado que ๐‘ฆ=3๐‘ฅ๐‘’๏Šญ๏Šฑ๏Šฌ, determine dd๐‘ฆ๐‘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‘’ + 2 1 ๐‘ฅ ๐‘’ ๏Šญ ๏Šฌ ๏Šฌ ๏Šฌ
  • D โˆ’ 1 8 ๐‘ฅ ๐‘’ + 3 ๐‘ฅ ๐‘’ ๏Šญ ๏Šฌ ๏Šฌ ๏Šฌ

Q11:

Encontre dd๐‘ฆ๐‘ฅ se ๐‘ฆ=2๐‘ฅ๏Šฑ๏Šญ.

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

Q12:

Dado que ๐‘ฆ=โˆ’25๐‘ฅ, determine dd๐‘ฆ๐‘ฅ.

Q13:

Calcule dd๐‘ฅ๏€พโˆš3๐‘ฅ+๐‘ฅ9+6๐œ‹๏Š๏Šญ๏Šฏ.

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

Q14:

Encontre a primeira derivada da funรงรฃo ๐‘“(๐‘ฅ)=โˆ’2๐‘ฅ+10.

Q15:

Encontre a primeira derivada da funรงรฃo ๐‘ฆ=๐‘ฅโˆ’๐‘ฅ4โˆ’3๐‘ฅ+6๏Šช๏Šฉ.

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

Q16:

Determine a primeira derivada da funรงรฃo ๐‘“(๐‘ฅ)=๏€น๐‘ฅ+8๏…๏€น3๐‘ฅโˆ’8๐‘ฅ+6๏…๏Šจ๏Šฉ.

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

Q17:

Determine dd๐‘ฆ๐‘ฅ, sabendo que ๐‘ฆ=โˆ’8๐‘ฅโˆ’4๐‘ฅ+3๐‘ฅ+5๏Šฏ๏Šซ.

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

Q18:

Calcule dd๐‘ฅ๏€นโˆ’3๐‘ฅโˆ’4๐‘ฅ+5๏…๏Šจ.

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

Q19:

Dado que ๐‘“(๐‘ฅ)=โˆ’๐‘ฅ+๐‘š๐‘ฅ+1๏Šจ, determine ๐‘š se ๐‘“โ€ฒ(3)=1.

Q20:

Se a funรงรฃo ๐‘“(๐‘ฅ)=โˆ’3๐‘ฅโˆ’5๏Šฏ, determine lim๏‚โ†’๏Šฆ๐‘“(๐‘ฅ+โ„Ž)โˆ’๐‘“(๐‘ฅ)โ„Ž.

  • A โˆ’ 2 7 ๐‘ฅ ๏Šฎ
  • B โˆ’ 2 7 ๐‘ฅ โˆ’ 5 โ„Ž ๏Šฎ
  • C โˆ’ 2 7
  • D โˆ’ 2 7 ๐‘ฅ ๏Šฏ
  • E โˆ’ 3 ๐‘ฅ ๏Šฏ

Q21:

Determine dd๐‘ฆ๐‘ฅ se ๐‘ฆ=6โˆš๐‘ฅ7 .

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

Q22:

Se ๐‘ฆ=5(2๐‘ฅ+2๐‘ฅ)cossen๏Šจ๏Šจ, determine dd๐‘ฆ๐‘ฅ.

Q23:

Se ๐‘ฆ=158๐‘ฅโˆ’158๐‘ฅsencos๏Šจ๏Šจ, determine dd๐‘ฆ๐‘ฅ.

  • A0
  • B 1 5 1 6 ๐‘ฅ s e n
  • C โˆ’ 1 5 1 6 ๐‘ฅ s e n
  • D โˆ’ 2 4 0 1 6 ๐‘ฅ s e n
  • E 2 4 0 1 6 ๐‘ฅ s e n

Q24:

Encontre dd๐‘ฆ๐‘ฅ, dado que ๐‘ฆ=โˆ’43๐‘ฅ๏Šฎ.

  • A โˆ’ 3 4 4 ๐‘ฅ ๏Šญ
  • B โˆ’ 3 4 4 ๐‘ฅ ๏Šฎ
  • C 3 4 4 ๐‘ฅ ๏Šฏ
  • D โˆ’ 4 3 ๐‘ฅ ๏Šญ

Q25:

Encontre dd๐‘ฆ๐‘ฅ, dado que ๐‘ฆ=3๐‘ฅ+4๐‘ฅ+6โˆ’7๐‘ฅโˆ’8๐‘ฅ๏Šช๏Šจ๏Šญ๏Šฎ.

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

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