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Atividade: Regras de Derivação

Q1:

Encontre d d 𝑦 π‘₯ , dado que 𝑦 = βˆ’ 4 3 π‘₯ 8 .

  • A βˆ’ 3 4 4 π‘₯ 8
  • B βˆ’ 3 4 4 π‘₯ 7
  • C βˆ’ 4 3 π‘₯ 7
  • D 3 4 4 π‘₯ 9

Q2:

Derive 𝑓 ( π‘₯ ) = βˆ’ 5 π‘Ž π‘₯ βˆ’ 9 𝑏 2 , onde π‘Ž e 𝑏 sΓ£o duas constantes.

  • A βˆ’ 5 π‘Ž π‘₯
  • B 1 0 π‘Ž π‘₯
  • C 5 π‘Ž π‘₯
  • D βˆ’ 1 0 π‘Ž π‘₯

Q3:

Derive 𝑓 ( π‘₯ ) = 2 π‘Ž π‘₯ + 𝑏 2 , onde π‘Ž e 𝑏 sΓ£o duas constantes.

  • A 2 π‘Ž π‘₯
  • B βˆ’ 4 π‘Ž π‘₯
  • C βˆ’ 2 π‘Ž π‘₯
  • D 4 π‘Ž π‘₯

Q4:

Determine a primeira derivada da função 𝑦 = √ π‘₯ + 7 √ π‘₯ 5 5 .

  • A 5 2 π‘₯ + 3 5 2 π‘₯ 3 2 7 2 βˆ’
  • B π‘₯ βˆ’ 7 π‘₯ 3 2 7 2 βˆ’
  • C 3 2 π‘₯ βˆ’ 2 1 2 π‘₯ 3 2 7 2 βˆ’
  • D 5 2 π‘₯ βˆ’ 3 5 2 π‘₯ 3 2 7 2 βˆ’

Q5:

Determine a primeira derivada da função 𝑦 = ο€Ή 3 π‘₯ + 7  ο€Ή 7 βˆ’ 3 π‘₯  5 5 .

  • A 9 0 π‘₯ 1 0
  • B 9 0 π‘₯ 9
  • C βˆ’ 1 8 π‘₯ 1 0
  • D βˆ’ 9 0 π‘₯ 9
  • E βˆ’ 9 0 π‘₯ 1 0

Q6:

Determine a primeira derivada da função 𝑦 = ( 5 π‘₯ + 2 ) ( 9 π‘₯ + 6 π‘₯ + 4 ) 2 3 .

  • A 4 5 π‘₯ + 4 8 π‘₯ + 2 0 π‘₯ 4 2
  • B 2 2 5 π‘₯ + 1 4 4 π‘₯ + 4 0 π‘₯ 5 3 2
  • C 2 2 5 π‘₯ + 1 4 4 π‘₯ + 4 0 π‘₯ 6 4 3
  • D 2 2 5 π‘₯ + 1 4 4 π‘₯ + 4 0 π‘₯ + 1 2 4 2

Q7:

Encontre a primeira derivada da função 𝑦 = 9 π‘₯ + 5 π‘₯ ο€Ό 4 π‘₯ + 5 π‘₯  2 2 .

  • A 4 0 0 π‘₯ + 4 0 0 π‘₯ + 1 2 5 π‘₯ + 9 4 βˆ’ 2
  • B 8 0 π‘₯ + 2 0 0 π‘₯ + 1 2 5 π‘₯ + 9 4 βˆ’ 2
  • C 3 2 0 π‘₯ + 2 0 0 π‘₯ βˆ’ 2 5 0 π‘₯ + 9 4 βˆ’ 2
  • D 4 0 0 π‘₯ + 4 0 0 π‘₯ βˆ’ 1 2 5 π‘₯ + 9 4 βˆ’ 2

Q8:

Calcule d d π‘₯ ο€Ώ βˆ’ 5 √ π‘₯  3 .

  • A βˆ’ 5 2 √ π‘₯ 3 4
  • B 5 √ π‘₯ 3 3 2
  • C βˆ’ 5 √ π‘₯ 3 4
  • D 5 3 √ π‘₯ 3 4

Q9:

Derive 𝑓 ( π‘₯ ) = 4 √ π‘₯ + 8 , e identifique o valor de π‘₯ para o qual a função NΓƒO Γ© derivΓ‘vel.

  • A 𝑓 β€² ( π‘₯ ) = 2 √ π‘₯ + 8 , a função nΓ£o Γ© derivΓ‘vel em π‘₯ β‰₯ 8 .
  • B 𝑓 β€² ( π‘₯ ) = 4 √ π‘₯ + 8 , a função nΓ£o Γ© derivΓ‘vel em π‘₯ β‰₯ 8 .
  • C 𝑓 β€² ( π‘₯ ) = 4 √ π‘₯ + 8 , a função nΓ£o Γ© derivΓ‘vel em π‘₯ β‰₯ βˆ’ 8 .
  • D 𝑓 β€² ( π‘₯ ) = 2 √ π‘₯ + 8 , a função nΓ£o Γ© derivΓ‘vel em π‘₯ β‰₯ βˆ’ 8 .

Q10:

Determine d d 𝑦 π‘₯ , sendo 𝑦 = √ π‘₯ 3 .

  • A 2 3 √ π‘₯ 3 4
  • B 1 3 √ π‘₯ 3
  • C 1 3 √ π‘₯ 3 4
  • D 1 3 ο„ž 1 π‘₯ 3 2

Q11:

Determine a primeira derivada de 𝑦 = 9 π‘₯ βˆ’ 7 √ π‘₯ 6 em ordem a π‘₯ .

  • A 5 4 π‘₯ βˆ’ 7 5
  • B 5 4 π‘₯ βˆ’ 7 √ π‘₯ 5
  • C 5 4 π‘₯ βˆ’ 7 2 π‘₯ 5
  • D 5 4 π‘₯ βˆ’ 7 2 √ π‘₯ 5
  • E 5 4 π‘₯ βˆ’ 7 π‘₯ 5

Q12:

Calcule d d π‘₯  βˆ’ 5 π‘₯  1 9 .

  • A βˆ’ 5 8 √ π‘₯ 9 8
  • B βˆ’ 5 √ π‘₯ 9 9 1 0
  • C βˆ’ 5 √ π‘₯ 9 8
  • D βˆ’ 5 9 √ π‘₯ 9 8

Q13:

Determine d d 𝑦 π‘₯ , sabendo que 𝑦 = 5 π‘₯ + 3 π‘₯ √ π‘₯ + √ 2 1 π‘₯ + 1 7 .

  • A 5 π‘₯ + 3 √ π‘₯ + √ 2 1 2
  • B βˆ’ 5 + 9 2 √ π‘₯ + √ 2 1 π‘₯ 5 2
  • C 5 π‘₯ + 9 2 √ π‘₯ + √ 2 1 π‘₯ 3
  • D βˆ’ 5 π‘₯ + 9 2 √ π‘₯ + √ 2 1 2