A Nagwa usa cookies para garantir que vocΓͺ tenha a melhor experiΓͺncia em nosso site. Saiba mais sobre nossa PolΓ­tica de privacidade.

Aula: Derivadas de Primeira Ordem Utilizando a Regra da Cadeia

Atividade • 23 Questões

Q1:

Se 𝑦 = ( 𝑧 + 1 1 ) 7 e 𝑧 = 5 π‘₯ + 8 2 , determine d d 𝑦 π‘₯ .

  • A 7 0 π‘₯ ο€Ή 5 π‘₯ + 1 9  2 6
  • B 7 ο€Ή 5 π‘₯ + 1 9  2 6
  • C 1 0 π‘₯ ο€Ή 5 π‘₯ + 1 9  2 6
  • D 3 5 π‘₯ ο€Ή 5 π‘₯ + 1 9  2 6

Q2:

Determine d d 𝑦 π‘₯ , sabendo que 𝑦 = ( 𝑧 + 9 ) 3 e 𝑧 = π‘₯ βˆ’ 9 4 .

  • A 1 2 π‘₯ 1 1
  • B 1 2 π‘₯ 1 3
  • C π‘₯ 1 3
  • D π‘₯ 1 1

Q3:

Se 𝑦 = ( 7 𝑧 + 3 ) 4 e 𝑧 = 1 7 2 π‘₯ c o t g , determine d d 𝑦 π‘₯ para π‘₯ = 3 πœ‹ 8 .

Q4:

Calcule d d 𝑦 π‘₯ em π‘₯ = 2 se 𝑦 = βˆ’ 𝑧  e 𝑧 = 6 π‘₯ βˆ’ 8 .

Q5:

Determine d d 𝑦 π‘₯ , sabendo que 𝑦 = 𝑧 2 e 𝑧 = 9 π‘₯ + 2 2 .

  • A 3 2 4 π‘₯ + 7 2 π‘₯ 3
  • B 3 6 π‘₯ + 7 2 π‘₯ 3
  • C 8 1 π‘₯ + 3 6 π‘₯ 3
  • D 2 4 3 π‘₯ + 3 6 π‘₯ 3

Q6:

Calcule d d 𝑦 π‘₯ para π‘₯ = 4 se 𝑦 = 𝑧 + 3 𝑧 + 1 3 e 𝑧 = π‘₯ βˆ’ 1 0 π‘₯ βˆ’ 3 .

  • A 1 0 7
  • B βˆ’ 1 0 7
  • C βˆ’ 1 0 4 9
  • D 1 0 4 9

Q7:

Dado que 𝑦 = √ 7 βˆ’ 4 𝑧 e 𝑧 = 2 π‘₯ t g , determine d d 𝑦 π‘₯ em π‘₯ = πœ‹ 8 .

  • A βˆ’ 8 √ 3 3
  • B βˆ’ 2 √ 3 3
  • C βˆ’ 8
  • D βˆ’ 1 6 √ 3 3

Q8:

Se 𝑦 = ( βˆ’ 8 𝑧 + 1 ) 3 e 𝑧 = 1 6 2 π‘₯ c o s , encontre d d 𝑦 π‘₯ quando π‘₯ = πœ‹ 4 .

  • A8
  • B βˆ’ 2 3
  • C βˆ’ 2 4
  • D βˆ’ 1 6 3

Q9:

Calcule d d 𝑦 π‘₯ em π‘₯ = 2 se 𝑦 = 2 √ 𝑧 + 9 √ 𝑧 e 𝑧 = 2 π‘₯ + 1  .

  • A 4 3
  • B2
  • C 1 3
  • D4
  • E 2 3

Q10:

Determine d d 𝑦 π‘₯ , sabendo que 𝑦 = 8 𝑧 + 1 𝑧 e π‘₯ 𝑧 = 9 .

  • A 1 9 βˆ’ 7 2 π‘₯ 2
  • B βˆ’ 1 8 1 π‘₯ βˆ’ 9 π‘₯ + 8 2 2
  • C 1 8 1 π‘₯ + 9 π‘₯ + 8 2 2
  • D 1 9 + 7 2 π‘₯ 2

Q11:

Dados que 𝑦 = 2 π‘₯ βˆ’ 2  e π‘₯ = 𝑧 βˆ’ 1  , determine d d d d 𝑦 𝑧 + 4 π‘₯ 𝑧 .

  • A 1 2 𝑧 
  • B 1 2 𝑧  
  • C 2 𝑧 + 2 𝑧   οŠͺ
  • D 2 𝑧 + 2 𝑧  

Q12:

Determine d d 𝑧 π‘₯ onde π‘₯ = 1 2 se 𝑧 = 𝑦 3 + 2 𝑦 + 1  e 𝑦 = βˆ’ 2 π‘₯ + π‘₯ βˆ’ 3  .

  • A βˆ’ 1 1
  • B βˆ’ 4 π‘₯ + 1
  • C βˆ’ 9 9
  • D 𝑦 + 2 

Q13:

Calcule d d 𝑦 π‘₯ em π‘₯ = βˆ’ 2 se 𝑦 = 𝑧 + 1 𝑧 βˆ’ 1 e 𝑧 = π‘₯ βˆ’ 1 π‘₯ + 1 .

  • A βˆ’ 1
  • B1
  • C βˆ’ 1 4
  • D 2 ( π‘₯ + 1 ) 2

Q14:

Calcule d d 𝑦 π‘₯ em π‘₯ = βˆ’ 3 se 𝑦 = 𝑧 βˆ’ 2 𝑧 + 2 e 𝑧 = π‘₯ + 2 π‘₯ βˆ’ 2 .

  • A βˆ’ 1 6 1 2 1
  • B 1 6 1 2 1
  • C βˆ’ 1 6 8 1
  • D βˆ’ 4 ( π‘₯ βˆ’ 2 ) 2

Q15:

Dado 𝑦 = βˆ’ 4 𝑧 + 3 2 𝑧 s e n e 𝑧 = βˆ’ 2 π‘₯ + πœ‹ , determine d d 𝑦 π‘₯ para π‘₯ = 0 .

Q16:

Calcule d d 𝑦 π‘₯ para π‘₯ = 4 se 𝑦 = 𝑧 βˆ’ 5 𝑧 + 1 2 e 𝑧 =  ( π‘₯ βˆ’ 3 ) 3 2 .

  • A βˆ’ 2
  • B βˆ’ 8 3
  • C βˆ’ 6
  • D βˆ’ 9 2

Q17:

Calcule d d 𝑦 π‘₯ em π‘₯ = 0 se 𝑦 = 5 √ 𝑧 e 𝑧 = π‘₯ + 1 6 π‘₯ + 1 .

  • A βˆ’ 7 5 8
  • B 1 1 0 √ 𝑧
  • C 8 5 8
  • D 1 1 2 5 6

Q18:

Determine d d 𝑦 π‘₯ para πœƒ = πœ‹ 6 , sabendo que π‘₯ = 7 5 πœƒ + 3 3 πœƒ c o s c o s 6 e 𝑦 = 3 2 πœƒ + 7 3 πœƒ s e n s e n 6 .

  • A βˆ’ 6 3 5
  • B βˆ’ 3 5 6
  • C βˆ’ 2 9 2
  • D βˆ’ 1 0 5 2

Q19:

Dados que 𝑦 = 𝑧 βˆ’ 8 𝑧 + 1 6 4 2 e 𝑧 = 2 5 π‘₯ s e n , determine d d 𝑦 π‘₯ .

  • A βˆ’ 3 2 0 5 π‘₯ 5 π‘₯ c o s s e n 3
  • B 3 2 0 5 π‘₯ 5 π‘₯ c o s s e n 3
  • C βˆ’ 3 2 0 5 π‘₯ c o s 3
  • D 3 2 0 5 π‘₯ s e n 3

Q20:

Calcule d d 𝑦 π‘₯ para π‘₯ = √ 3 se 𝑦 = ( βˆ’ 2 + π‘₯ ) ( βˆ’ 2 βˆ’ π‘₯ ) 4 4 .

  • A βˆ’ 8 √ 3
  • B 4 √ 3
  • C βˆ’ √ 3
  • D βˆ’ 2 √ 3

Q21:

Dados que 𝑦 = πœ‹ 𝑧 3 6 c o t g e 𝑧 = 6 √ π‘₯ , determine d d 𝑦 π‘₯ para π‘₯ = 4 .

  • A βˆ’ πœ‹ 1 8
  • B βˆ’ πœ‹ 1 6
  • C 3 4
  • D βˆ’ πœ‹ 9

Q22:

Calcule d d 𝑦 𝑧 para 𝑧 = 3 se 𝑦 = π‘₯ βˆ’ 3 π‘₯ + 3 e π‘₯ = 3 𝑧 + 4 .

  • A 9 1 2 8
  • B 8 1 1 2 8
  • C βˆ’ 9 1 2 8
  • D βˆ’ 8 1 1 2 8

Q23:

Dado que 𝑦 = 8 𝑧 βˆ’ 6 𝑧 βˆ’ 9  e 𝑧 = 3 π‘₯ βˆ’ 2 7 π‘₯ , determine d d 𝑦 π‘₯ quando π‘₯ = βˆ’ 3 .

  • A βˆ’ 3 6
  • B βˆ’ 1 2
  • C βˆ’ 6
  • D0
  • E6
Visualizar