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Aula: Encontrando Derivadas de Ordem Superior Implicitamente

Atividade • 24 Questões

Q1:

Dado que π‘₯ + 3 𝑦 = 3 2 2 , determine 𝑦 β€² β€² por derivação implΓ­cita.

  • A 𝑦 = βˆ’ 1 3 𝑦 β€² β€² 3
  • B 𝑦 = 1 3 𝑦 β€² β€² 3
  • C 𝑦 = βˆ’ 𝑦 + 1 1 2 𝑦 β€² β€² 2 2
  • D 𝑦 = 2 𝑦 βˆ’ 1 3 𝑦 β€² β€² 2 3
  • E 𝑦 = βˆ’ 2 π‘₯ + 3 9 𝑦 β€² β€² 2 2

Q2:

Dado π‘₯ + 9 = βˆ’ 2 π‘₯ 𝑦 2 , determine π‘₯ 𝑦 π‘₯ + 2 𝑦 π‘₯ d d d d 2 2 .

  • A βˆ’ 1
  • B2
  • C βˆ’ 4
  • D βˆ’ 1 2

Q3:

Dado π‘₯ βˆ’ 5 = 7 π‘₯ 𝑦 2 , determine π‘₯ 𝑦 π‘₯ + 2 𝑦 π‘₯ d d d d 2 2 .

  • A 2 7
  • B2
  • C14
  • D 1 7

Q4:

Encontre d d 𝑦 π‘₯ por derivação implΓ­cita se βˆ’ 𝑒 π‘₯ = 4 π‘₯ 𝑦 + 2 π‘₯ 𝑦 s e n .

  • A βˆ’ 𝑒 π‘₯ + 4 𝑦 + 2 𝑒 π‘₯ + 4 π‘₯ 𝑦 𝑦 c o s s e n
  • B 𝑒 π‘₯ βˆ’ 4 𝑦 𝑒 π‘₯ + 4 π‘₯ 𝑦 𝑦 c o s s e n
  • C 𝑒 π‘₯ βˆ’ 4 𝑦 βˆ’ 2 𝑒 π‘₯ + 4 π‘₯ 𝑦 𝑦 c o s s e n
  • D βˆ’ 𝑒 π‘₯ + 4 𝑦 𝑒 π‘₯ + 4 π‘₯ 𝑦 𝑦 c o s s e n
  • E 𝑒 π‘₯ + 4 𝑦 + 2 𝑒 π‘₯ + 4 π‘₯ 𝑦 𝑦 c o s s e n

Q5:

Dado que 2 π‘₯ βˆ’ π‘₯ 𝑦 βˆ’ 𝑦 = βˆ’ 1 2 2 , determine 𝑦 β€² β€² por derivação implΓ­cita.

  • A 𝑦 = βˆ’ 9 π‘₯ 𝑦 β€² βˆ’ 9 𝑦 ( 2 𝑦 + π‘₯ ) β€² β€² 2
  • B 𝑦 = 9 π‘₯ βˆ’ 9 𝑦 ( 2 𝑦 + π‘₯ ) β€² β€² 2
  • C 𝑦 = βˆ’ 7 π‘₯ 𝑦 β€² βˆ’ 7 𝑦 ( 2 𝑦 + π‘₯ ) β€² β€² 2
  • D 𝑦 = βˆ’ 9 π‘₯ βˆ’ 9 𝑦 ( 2 𝑦 + π‘₯ ) β€² β€² 2
  • E 𝑦 = 9 π‘₯ 𝑦 β€² βˆ’ 9 𝑦 ( 2 𝑦 + π‘₯ ) β€² β€² 2

Q6:

Dado que π‘₯ + 3 π‘₯ 𝑦 βˆ’ 5 𝑦 = βˆ’ 2 2 2 , determine 𝑦 β€² β€² por derivação implΓ­cita.

  • A 𝑦 = βˆ’ 2 9 π‘₯ 𝑦 β€² βˆ’ 2 9 𝑦 ( βˆ’ 1 0 𝑦 + 3 π‘₯ ) β€² β€² 2
  • B 𝑦 = 2 9 π‘₯ βˆ’ 2 9 𝑦 ( βˆ’ 1 0 𝑦 + 3 π‘₯ ) β€² β€² 2
  • C 𝑦 = βˆ’ 1 1 π‘₯ 𝑦 β€² βˆ’ 1 1 𝑦 ( βˆ’ 1 0 𝑦 + 3 π‘₯ ) β€² β€² 2
  • D 𝑦 = βˆ’ 2 9 π‘₯ βˆ’ 2 9 𝑦 ( βˆ’ 1 0 𝑦 + 3 π‘₯ ) β€² β€² 2
  • E 𝑦 = 2 9 π‘₯ 𝑦 β€² βˆ’ 2 9 𝑦 ( βˆ’ 1 0 𝑦 + 3 π‘₯ ) β€² β€² 2

Q7:

Se 𝑒 = 5 π‘₯ βˆ’ 4 𝑦  ο‘‘ , determine d d 𝑦 π‘₯ por derivação implΓ­cita.

  • A d d 𝑦 π‘₯ = 𝑦 ο€½ 5 𝑦 βˆ’ 𝑒  ο€½ 4 𝑦 βˆ’ π‘₯ 𝑒   ο‘‘  ο‘‘ 
  • B d d 𝑦 π‘₯ = βˆ’ 𝑦 ο€½ 5 𝑦 βˆ’ 𝑒  ο€½ 4 𝑦 βˆ’ π‘₯ 𝑒   ο‘‘  ο‘‘ 
  • C d d 𝑦 π‘₯ = βˆ’ 𝑦 ο€½ 𝑦 βˆ’ 𝑒  π‘₯ 𝑒  ο‘‘  ο‘‘
  • D d d 𝑦 π‘₯ = 𝑦 ο€½ 5 𝑦 + 𝑒  ο€½ 4 𝑦 + π‘₯ 𝑒   ο‘‘  ο‘‘ 
  • E d d 𝑦 π‘₯ = 𝑦 ο€½ 5 𝑦 βˆ’ 𝑒 + π‘₯ 𝑒  4 𝑦  ο‘‘  ο‘‘ 

Q8:

Dado βˆ’ 8 π‘₯ βˆ’ 3 π‘₯ βˆ’ 5 𝑦 = 0 2 2 , determine 𝑦 𝑦 π‘₯ + ο€½ 𝑦 π‘₯  d d d d 2 2 2 .

  • A βˆ’ 8 5
  • B16
  • C 8 5
  • D βˆ’ 8

Q9:

Se π‘₯ + π‘₯ 𝑦 + 𝑦 = 1 2 3 , determine o valor de 𝑦 β€² β€² β€² para π‘₯ = 1 .

Q10:

Dado π‘₯ βˆ’ 3 𝑦 = βˆ’ 4 3 3 , determine 𝑦 β€² β€² por derivação implΓ­cita.

  • A 𝑦 = βˆ’ 2 π‘₯ + 6 π‘₯ 𝑦 9 𝑦 β€² β€² 4 3 5
  • B 𝑦 = βˆ’ 2 π‘₯ + 2 π‘₯ 𝑦 3 𝑦 β€² β€² 2 3
  • C 𝑦 = βˆ’ π‘₯ + π‘₯ 𝑦 3 𝑦 β€² β€² 2 3
  • D 𝑦 = βˆ’ π‘₯ + 3 π‘₯ 𝑦 9 𝑦 β€² β€² 4 3 4
  • E 𝑦 = βˆ’ π‘₯ + 3 π‘₯ 𝑦 3 𝑦 β€² β€² 5 3 2 3

Q11:

Encontre d d 3 3 𝑦 π‘₯ , dados que 6 π‘₯ + 6 𝑦 = 2 5 2 2 .

  • A βˆ’ 2 5 π‘₯ 2 𝑦 5
  • B βˆ’ π‘₯ 2 𝑦 5
  • C βˆ’ 2 5 π‘₯ 2 𝑦 6
  • D βˆ’ 7 5 π‘₯ 𝑦 5

Q12:

Seja βˆ’ 7 π‘Ž π‘₯ + 5 𝑏 π‘₯ + 𝑦 = 9 𝑐 3 2 , onde π‘Ž , 𝑏 , e 𝑐 sΓ£o constantes. Determine 𝑦 ο€Ώ 𝑦 π‘₯  + ο€½ 𝑦 π‘₯  βˆ’ 2 1 π‘Ž π‘₯ d d d d 2 2 2 .

Q13:

Dado que s e n c o s 𝑦 + 2 π‘₯ = 5 , determine 𝑦 β€² β€² por derivação implΓ­cita.

  • A 𝑦 = 4 π‘₯ 𝑦 + 2 π‘₯ 𝑦 𝑦 β€² β€² 2 2 3 s e n s e n c o s c o s c o s
  • B 𝑦 = 2 π‘₯ 𝑦 + 2 π‘₯ 𝑦 𝑦 β€² β€² 2 s e n s e n c o s c o s c o s
  • C 𝑦 = βˆ’ 4 π‘₯ 𝑦 + 2 π‘₯ 𝑦 𝑦 β€² β€² 2 2 3 s e n s e n c o s c o s c o s
  • D 𝑦 = βˆ’ 4 π‘₯ 𝑦 + 2 π‘₯ 𝑦 𝑦 β€² β€² 2 2 3 s e n s e n c o s c o s c o s
  • E 𝑦 = 2 π‘₯ 𝑦 βˆ’ 2 π‘₯ 𝑦 𝑦 β€² β€² 2 s e n s e n c o s c o s c o s

Q14:

Dado βˆ’ 7 π‘₯ βˆ’ 7 𝑦 = 1 0 2 2 , determine 𝑦 𝑦 βˆ’ 1 0 7 3 β€² β€² .

Q15:

Se 2 π‘₯ 𝑦 = βˆ’ 1 7 5 π‘₯ 5 π‘₯ s e n c o s , encontre π‘₯ ο€Ώ 𝑦 π‘₯  + 2 ο€½ 𝑦 π‘₯  d d d d   .

  • A βˆ’ 1 0 0 π‘₯ 𝑦
  • B βˆ’ 2 5 π‘₯ 𝑦
  • C βˆ’ 5 0 π‘₯ 𝑦
  • D βˆ’ 1 0 0 π‘₯ 𝑦

Q16:

Dado que 9 π‘₯ 𝑒 + 𝑦 𝑒 = 7    ο‘‘     , encontre d d 𝑦 π‘₯ quando π‘₯ = 0 .

  • A 5 6 𝑒 βˆ’ 4 5 5 𝑒  
  • B 5 6 𝑒 βˆ’ 4 5 5 
  • C 𝑒 βˆ’ 4 5 5 𝑒  
  • D 5 6 𝑒 βˆ’ 4 5 𝑒  

Q17:

Dado ( 6 π‘₯ + 7 𝑦 ) = 4 7 , determine d d d d 2 2 𝑦 π‘₯ + 𝑦 π‘₯ .

  • A βˆ’ 6 7
  • B 6 7
  • C βˆ’ 2 7
  • D0

Q18:

Dado 7 𝑒 π‘₯ = 8 𝑦 + 5 π‘₯  οŠͺ    s e n , determine d d 𝑦 π‘₯ em π‘₯ = 0 .

  • A 7 8
  • B βˆ’ 1 8
  • C0
  • D βˆ’ 7 2

Q19:

Se βˆ’ 1 0 π‘₯ 𝑦 βˆ’ 5 = π‘₯ 2 , determine π‘₯ ο€Ώ 𝑦 π‘₯  + 2 ο€½ 𝑦 π‘₯  d d d d 2 2 .

  • A βˆ’ 1 5
  • B 1 5
  • C 2 + 𝑦 βˆ’ 1 5 π‘₯
  • D βˆ’ 2 5 βˆ’ 𝑦 π‘₯
  • E βˆ’ 2 5 + 𝑦 π‘₯

Q20:

Suponha que 𝑒 βˆ’ 2 π‘₯ 𝑦 = 𝑒    . Encontre 𝑦   quando π‘₯ = 0 .

  • A 𝑦 = βˆ’ 3 2 𝑒   
  • B 𝑦 = 3 𝑒 4 βˆ’ 3 𝑒    
  • C 𝑦 = βˆ’ 9 2 𝑒   
  • D 𝑦 = βˆ’ 6 𝑒 + 3 2 𝑒    
  • E 𝑦 = βˆ’ 3 𝑒 4 βˆ’ 3 𝑒    

Q21:

Dado que , encontre .

  • A
  • B
  • C
  • D

Q22:

Dado que , encontre .

  • A
  • B
  • C
  • D

Q23:

Sendo 𝑒 𝑦 + 3 𝑒 π‘₯ = 5   ο‘‘  , determine d d 𝑦 π‘₯ para π‘₯ = 0 .

  • A βˆ’ 3 𝑒 βˆ’ 1
  • B βˆ’ 3 𝑒 βˆ’ 5
  • C 1 5 𝑒 + 5
  • D 3 𝑒 + 1

Q24:

Se 8 π‘₯ 𝑦 = 7 4 π‘₯ s e n , determine π‘₯ 𝑦 π‘₯ + 2 𝑦 π‘₯ d d d d 2 2 .

  • A βˆ’ 1 4 4 π‘₯ s e n
  • B 1 4 4 π‘₯ s e n
  • C βˆ’ 7 8 4 π‘₯ s e n
  • D 7 2 4 π‘₯ s e n
  • E βˆ’ 7 2 4 π‘₯ s e n
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