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Comece a praticar

Atividade: Encontrando as Derivadas de Funções Paramétricas

Q1:

Dado que π‘₯ = 3 𝑑 + 1 3 e 𝑦 = 5 𝑑 βˆ’ 𝑑 2 , encontre d d 𝑦 π‘₯ .

  • A 9 𝑑 1 0 𝑑 βˆ’ 1 2
  • B 9 𝑑 ( 1 0 𝑑 βˆ’ 1 ) 2
  • C 3 𝑑 5 𝑑 βˆ’ 1 2
  • D 1 0 𝑑 βˆ’ 1 9 𝑑 2
  • E 3 𝑑 ( 5 𝑑 βˆ’ 1 ) 2

Q2:

Dado que π‘₯ = 4 𝑑 + 1 2 e 𝑦 = 4 𝑑 + 5 𝑑 2 , encontre d d 𝑦 π‘₯ .

  • A 8 𝑑 8 𝑑 + 5
  • B 8 𝑑 ( 8 𝑑 + 5 )
  • C 4 𝑑 + 5 4 𝑑
  • D 8 𝑑 + 5 8 𝑑
  • E 4 𝑑 ( 4 𝑑 + 5 )

Q3:

Dado que π‘₯ = 3 𝑒 5 𝑑 e 𝑦 = 𝑑 𝑒 βˆ’ 5 𝑑 , encontre d d 𝑦 π‘₯ .

  • A 1 5 𝑒 1 βˆ’ 5 𝑑 1 0 𝑑
  • B 1 5 ( 1 βˆ’ 5 𝑑 )
  • C 5 𝑑 βˆ’ 1 1 5 𝑒 1 0 𝑑
  • D 1 βˆ’ 5 𝑑 1 5 𝑒 1 0 𝑑
  • E 1 5 ( 5 𝑑 βˆ’ 1 )

Q4:

Dado que π‘₯ = 5 𝑑 βˆ’ 4 𝑑 l n e 𝑦 = 4 𝑑 + 5 3 𝑑 l n , encontre d d 𝑦 π‘₯ .

  • A 5 𝑑 βˆ’ 4 4 𝑑 + 5
  • B ( 4 𝑑 + 5 ) ( 5 𝑑 βˆ’ 4 ) 𝑑 2
  • C 4 𝑑 + 5 3 ( 5 𝑑 βˆ’ 4 )
  • D 4 𝑑 + 5 5 𝑑 βˆ’ 4
  • E ( 4 𝑑 + 5 ) ( 5 𝑑 βˆ’ 4 ) 3 𝑑 2

Q5:

Dado que π‘₯ = 𝑑 βˆ’ 𝑑 l n e 𝑦 = 𝑑 + 𝑑 l n , encontre d d 2 2 𝑦 π‘₯ .

  • A βˆ’ ( 𝑑 βˆ’ 1 ) 2 𝑑 3
  • B βˆ’ 2 𝑑 ( 𝑑 βˆ’ 1 )
  • C βˆ’ 1 𝑑 ( 𝑑 βˆ’ 1 )
  • D βˆ’ 2 𝑑 ( 𝑑 βˆ’ 1 ) 3
  • E βˆ’ 2 ( 𝑑 βˆ’ 1 ) 2

Q6:

Dado que π‘₯ = 2 𝑑 βˆ’ 3 3 𝑑 l n e 𝑦 = 3 𝑑 + 4 2 𝑑 l n , encontre d d 2 2 𝑦 π‘₯ .

  • A βˆ’ ( 2 𝑑 βˆ’ 3 ) 1 7 𝑑 3
  • B βˆ’ 1 7 𝑑 ( 2 𝑑 βˆ’ 3 )
  • C βˆ’ 4 𝑑 ( 2 𝑑 βˆ’ 3 )
  • D βˆ’ 1 7 𝑑 ( 2 𝑑 βˆ’ 3 ) 3
  • E βˆ’ 1 7 ( 2 𝑑 βˆ’ 3 ) 2

Q7:

Sendo 𝑦 = √ 4 π‘₯ βˆ’ 5 2 e 𝑧 = 5 π‘₯ + 9 2 , determine 𝑦 ο€½ 𝑦 π‘₯  + 𝑧 π‘₯ d d d d .

  • A14
  • B 6 π‘₯
  • C 1 4 π‘₯ + 𝑦
  • D 1 4 π‘₯
  • E 1 4 𝑦 + 𝑧

Q8:

Uma curva tem equaçáes paramΓ©tricas π‘₯ = 7 π‘š + 5 π‘š + π‘š + 4   e 𝑦 = 6 π‘š βˆ’ 6 π‘š βˆ’ 8  . Determine π‘š para o qual a tangente Γ© horizontal.

  • A βˆ’ 1 3
  • B βˆ’ 1 7
  • C βˆ’ 1 7 , βˆ’ 1 3
  • D 1 2

Q9:

Dado que π‘₯ = 2 𝑑 4 + 𝑑 e 𝑦 = √ 4 + 𝑑 , encontre d d 𝑦 π‘₯ .

  • A 1 6 ( 4 + 𝑑 ) 5 2
  • B 4 ( 4 + 𝑑 ) 5 2
  • C 1 6 ( 4 + 𝑑 ) 5 2
  • D 1 1 6 ( 4 + 𝑑 ) 3 2
  • E 1 8 ( 4 + 𝑑 ) 3 2

Q10:

Suponha π‘₯ = βˆ’ 3 5 πœƒ + 1 3 s e c 2 e 𝑦 = βˆ’ 3 5 πœƒ βˆ’ 1 4 t g . Encontre d d 𝑦 π‘₯ quando πœƒ = πœ‹ 4 .

  • A βˆ’ 1 2
  • B1
  • C βˆ’ 5 2
  • D 1 2

Q11:

Se 𝑦 = βˆ’ 5 π‘₯ βˆ’ 7 3 e 𝑧 = 3 π‘₯ + 1 6 2 , determine 𝑑 𝑧 𝑑 𝑦 2 2 para π‘₯ = 1 .

  • A βˆ’ 2 5
  • B 2 5
  • C βˆ’ 5 2
  • D βˆ’ 2 7 5
  • E 2 7 5

Q12:

Determine a equação da tangente Γ  curva π‘₯ = 5 πœƒ s e c e 𝑦 = 5 πœƒ t g em πœƒ = πœ‹ 6 .

  • A 2 𝑦 βˆ’ π‘₯ = 0
  • B 𝑦 + 2 π‘₯ βˆ’ 2 5 √ 3 3 = 0
  • C βˆ’ 2 𝑦 βˆ’ π‘₯ + 2 0 √ 3 3 = 0
  • D 𝑦 βˆ’ 2 π‘₯ + 5 √ 3 = 0

Q13:

Se π‘₯ = βˆ’ 8 𝑑 βˆ’ 8 5 e 𝑦 = √ 𝑑 5 6 , encontre d d 𝑦 π‘₯ para 𝑑 = 1 .

Q14:

Dado que π‘₯ = 3 𝑑 + 1 2 e 𝑦 = 3 𝑑 + 5 𝑑 2 , encontre d d 2 2 𝑦 π‘₯ .

  • A βˆ’ 5 𝑑
  • B 5 3 6 𝑑 3
  • C 5 𝑑
  • D βˆ’ 5 3 6 𝑑 3
  • E βˆ’ 5 6 𝑑 ( 6 𝑑 + 5 ) 2

Q15:

Se 𝑦 = π‘₯ √ 5 + π‘₯  e 𝑧 = √ 5 + π‘₯ 5 π‘₯  , encontre 5 𝑧 𝑦 π‘₯ + 𝑧 π‘₯  d d d d .