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Atividade: Diferenciação de Funções Trigonométricas

Q1:

Determine d d ๐‘ฆ ๐‘ฅ , dado ๐‘ฆ = 2 2 ๐‘ฅ s e n .

  • A โˆ’ 4 2 ๐‘ฅ c o s
  • B 2 2 ๐‘ฅ c o s
  • C c o s 2 ๐‘ฅ
  • D 4 2 ๐‘ฅ c o s

Q2:

Determine d d ๐‘ฆ ๐‘ฅ , dado ๐‘ฆ = 6 3 ๐‘ฅ s e n .

  • A โˆ’ 1 8 3 ๐‘ฅ c o s
  • B 6 3 ๐‘ฅ c o s
  • C c o s 3 ๐‘ฅ
  • D 1 8 3 ๐‘ฅ c o s
  • E 3 3 ๐‘ฅ c o s

Q3:

Se ๐‘ฆ = 7 2 ๐‘ฅ t g , determine d d ๐‘ฆ ๐‘ฅ .

  • A โˆ’ 1 4 2 ๐‘ฅ s e c 2
  • B 1 4 2 ๐‘ฅ s e c
  • C 7 2 ๐‘ฅ s e c 2
  • D 1 4 2 ๐‘ฅ s e c 2
  • E s e c 2 2 ๐‘ฅ

Q4:

Dado ๐‘ฆ = 1 0 ๐‘ฅ โˆ’ 2 9 ๐‘ฅ c o s , determine d d ๐‘ฆ ๐‘ฅ .

  • A 1 0 + 1 8 9 ๐‘ฅ c o s
  • B 1 0 + 2 9 ๐‘ฅ s e n
  • C 1 0 ๐‘ฅ + 1 8 9 ๐‘ฅ s e n
  • D 1 0 + 1 8 9 ๐‘ฅ s e n

Q5:

Sendo ๐‘ฆ = 5 ๐‘ฅ + ๏€ป ๏‡ 1 โˆ’ 5 ๐‘ฅ ๏€ป ๏‡ t g t g t g t g ๏Ž„ ๏Šญ ๏Ž„ ๏Šญ , determine d d ๐‘ฆ ๐‘ฅ .

  • A s e c ๏Šจ ๏€ป 5 ๐‘ฅ + ๐œ‹ 7 ๏‡
  • B 5 ๏€ป 5 ๐‘ฅ โˆ’ ๐œ‹ 7 ๏‡ s e c ๏Šจ
  • C 5 ๏€ป 5 ๐‘ฅ + ๐œ‹ 7 ๏‡ s e c
  • D 5 ๏€ป 5 ๐‘ฅ + ๐œ‹ 7 ๏‡ s e c ๏Šจ
  • E 5 ๏€ป 5 ๐‘ฅ โˆ’ ๐œ‹ 7 ๏‡ s e c

Q6:

Determine a primeira derivada da funรงรฃo ๐‘“ ( ๐‘ฅ ) = โˆ’ 2 ( 9 ๐‘ฅ โˆ’ 4 ) ( 9 ๐‘ฅ โˆ’ 4 ) s e n c o s .

  • A โˆ’ 2 ( 1 8 ๐‘ฅ โˆ’ 8 ) s e n
  • B 1 8 ( 1 8 ๐‘ฅ โˆ’ 8 ) c o s
  • C 2 ( 1 8 ๐‘ฅ โˆ’ 8 ) s e n
  • D โˆ’ 1 8 ( 1 8 ๐‘ฅ โˆ’ 8 ) c o s

Q7:

Se ๐‘ฆ = ๏„ ๏€น 2 + 4 ๐‘ฅ ๏… ๏Žข t g ๏Šญ ๏Šฎ , encontre d d ๐‘ฆ ๐‘ฅ .

  • A 2 2 4 3 ๏„ ๏€น 2 + 4 ๐‘ฅ ๏… ๐‘ฅ ๐‘ฅ ๏Žข t g t g s e c ๏Šญ ๏Šซ ๏Šญ
  • B 7 3 ๏„ ๏€น 2 + 4 ๐‘ฅ ๏… ๐‘ฅ ๐‘ฅ ๏Žข t g t g s e c ๏Šญ ๏Šง ๏Šง ๏Šฌ ๏Šจ
  • C 2 2 4 3 ๏„ ๏€น 2 + 4 ๐‘ฅ ๏… ๐‘ฅ ๐‘ฅ ๏Žข t g t g s e c ๏Šญ ๏Šฎ ๏Šฎ
  • D 2 2 4 3 ๏„ ๏€น 2 + 4 ๐‘ฅ ๏… ๐‘ฅ ๐‘ฅ ๏Žข t g t g s e c ๏Šญ ๏Šซ ๏Šฌ ๏Šจ

Q8:

Se ๐‘ฆ = 3 ( 8 ๐‘ฅ โˆ’ 3 ) c o s , determine d d ๐‘ฆ ๐‘ฅ .

  • A โˆ’ 8 ( 8 ๐‘ฅ โˆ’ 3 ) s e n
  • B โˆ’ ( 8 ๐‘ฅ โˆ’ 3 ) s e n
  • C โˆ’ 3 ( 8 ๐‘ฅ โˆ’ 3 ) s e n
  • D โˆ’ 2 4 ( 8 ๐‘ฅ โˆ’ 3 ) s e n
  • E 2 4 ( 8 ๐‘ฅ โˆ’ 3 ) s e n

Q9:

Dado ๐‘ฆ = 4 ๐‘ฅ 4 ๐‘ฅ s e n t g , encontre d d ๐‘ฆ ๐‘ฅ em ๐‘ฅ = ๐œ‹ 6 .

  • A โˆ’ 2 + 2 โˆš 3
  • B 5 โˆš 3 2
  • C โˆ’ 6 โˆš 3
  • D 1 0 โˆš 3

Q10:

Dado que ๐‘ฆ = ( โˆ’ 2 ๐‘ฅ โˆ’ 7 ) ( 8 ๐‘ฅ + 1 9 ) c o s s e n , determine d d ๐‘ฆ ๐‘ฅ para ๐‘ฅ = ๐œ‹ .

Q11:

Se ๐‘ฆ = ( 4 ๐‘ฅ โˆ’ 8 ) + ( 8 ๐‘ฅ + 6 ) s e n c o s , determine d d ๐‘ฆ ๐‘ฅ .

  • A 4 ( 4 ๐‘ฅ โˆ’ 8 ) โˆ’ 8 ( 8 ๐‘ฅ + 6 ) s e n c o s
  • B 8 ( 8 ๐‘ฅ + 6 ) โˆ’ 4 ( 4 ๐‘ฅ โˆ’ 8 ) s e n c o s
  • C โˆ’ ( 8 ๐‘ฅ + 6 ) โˆ’ ( 4 ๐‘ฅ โˆ’ 8 ) s e n c o s
  • D โˆ’ 8 ( 8 ๐‘ฅ + 6 ) + 4 ( 4 ๐‘ฅ โˆ’ 8 ) s e n c o s

Q12:

Se ๐‘ฆ = ( 8 ๐‘ฅ โˆ’ 4 ) s e n 2 , determine d d ๐‘ฆ ๐‘ฅ .

  • A โˆ’ 1 6 ๐‘ฅ ( 8 ๐‘ฅ โˆ’ 4 ) c o s 2
  • B โˆ’ ( 8 ๐‘ฅ โˆ’ 4 ) c o s 2
  • C 1 6 ๐‘ฅ ( 8 ๐‘ฅ โˆ’ 4 ) s e n 2
  • D 1 6 ๐‘ฅ ( 8 ๐‘ฅ โˆ’ 4 ) c o s 2

Q13:

Se ๐‘ฆ = ๐‘ฅ 5 ๐‘ฅ 5 s e n , determine d d ๐‘ฆ ๐‘ฅ .

  • A โˆ’ 5 ๐‘ฅ 5 ๐‘ฅ + 5 ๐‘ฅ 5 ๐‘ฅ 5 4 c o s s e n
  • B 5 ๐‘ฅ + 5 5 ๐‘ฅ 4 c o s
  • C 5 ๐‘ฅ 5 ๐‘ฅ โˆ’ 5 ๐‘ฅ 5 ๐‘ฅ 5 4 c o s s e n
  • D 5 ๐‘ฅ 5 ๐‘ฅ + 5 ๐‘ฅ 5 ๐‘ฅ 5 4 c o s s e n
  • E 2 5 ๐‘ฅ 5 ๐‘ฅ 4 c o s

Q14:

Se ๐‘ฆ = 7 ๐‘ฅ ( 5 ๐‘ฅ + 4 ) s e n , determine d d ๐‘ฆ ๐‘ฅ .

  • A 7 ๐‘ฅ ( 5 ๐‘ฅ + 4 ) + 7 ( 5 ๐‘ฅ + 4 ) c o s s e n
  • B โˆ’ 3 5 ๐‘ฅ ( 5 ๐‘ฅ + 4 ) + 7 ( 5 ๐‘ฅ + 4 ) c o s s e n
  • C 5 ( 5 ๐‘ฅ + 4 ) + 7 c o s
  • D 3 5 ๐‘ฅ ( 5 ๐‘ฅ + 4 ) + 7 ( 5 ๐‘ฅ + 4 ) c o s s e n
  • E 5 ๐‘ฅ ( 5 ๐‘ฅ + 4 ) + 7 ( 5 ๐‘ฅ + 4 ) c o s s e n

Q15:

Se ๐‘ฆ = 1 5 8 ๐‘ฅ โˆ’ 1 5 8 ๐‘ฅ s e n c o s 2 2 , determine d d ๐‘ฆ ๐‘ฅ .

  • A 1 5 1 6 ๐‘ฅ s e n
  • B โˆ’ 2 4 0 1 6 ๐‘ฅ s e n
  • C โˆ’ 1 5 1 6 ๐‘ฅ s e n
  • D 2 4 0 1 6 ๐‘ฅ s e n
  • E0

Q16:

Se ๐‘ฆ = 6 ๐‘ฅ 1 โˆ’ 6 ๐‘ฅ c o s s e n , determine d d ๐‘ฆ ๐‘ฅ .

  • A 6 ( 1 โˆ’ 6 ๐‘ฅ ) s e n 2
  • B โˆ’ 6 1 โˆ’ 6 ๐‘ฅ s e n
  • C 1 ( 1 โˆ’ 6 ๐‘ฅ ) s e n 2
  • D 6 1 โˆ’ 6 ๐‘ฅ s e n
  • E โˆ’ 6 ๐‘ฅ ( 1 โˆ’ 6 ๐‘ฅ ) s e n s e n 2

Q17:

Se ๐‘ฆ = 5 2 ๐‘ฅ c o s 3 , determine d d ๐‘ฆ ๐‘ฅ .

  • A โˆ’ 5 2 ๐‘ฅ 2 ๐‘ฅ c o s s e n 2
  • B 3 0 2 ๐‘ฅ c o s 2
  • C 3 0 2 ๐‘ฅ s e n 2
  • D โˆ’ 3 0 2 ๐‘ฅ 2 ๐‘ฅ c o s s e n 2
  • E โˆ’ 3 0 2 ๐‘ฅ 2 ๐‘ฅ c o s s e n 4

Q18:

Se ๐‘ฆ = ๐‘ฅ 1 โˆ’ ๐‘ฅ s e n c o s , qual das seguintes alternativas รฉ o mesmo que ๐‘ฆ โ€ฒ ?

  • A 2 ๐‘ฆ ๐‘ฅ c o s s e c
  • B ๐‘ฆ ๐‘ฅ c o s s e c
  • C ๐‘ฆ
  • D โˆ’ ๐‘ฆ ๐‘ฅ c o s s e c

Q19:

Se ๐‘ฆ = 9 ๐‘ฅ 5 + 5 ๐‘ฅ s e n c o s 2 , encontre d d ๐‘ฆ ๐‘ฅ .

  • A โˆ’ 9 5 ๐‘ฅ s e n 2
  • B โˆ’ 9 5 ๐‘ฅ s e n
  • C 9 5 ๐‘ฅ s e n 2
  • D 9 5 ๐‘ฅ s e n

Q20:

Se ๐‘ฆ = 6 4 ๐‘ฅ + 2 2 ๐‘ฅ c o s s e n , determine d d ๐‘ฆ ๐‘ฅ .

  • A โˆ’ 6 4 ๐‘ฅ + 4 2 ๐‘ฅ s e n c o s
  • B 2 4 4 ๐‘ฅ โˆ’ 4 2 ๐‘ฅ s e n c o s
  • C โˆ’ 2 4 4 ๐‘ฅ โˆ’ 4 2 ๐‘ฅ c o s s e n
  • D โˆ’ 2 4 4 ๐‘ฅ + 4 2 ๐‘ฅ s e n c o s

Q21:

Se ๐‘ฆ = ( 1 2 5 ๐‘ฅ ) c o s c o s , determine d d ๐‘ฆ ๐‘ฅ .

  • A 1 2 ( 1 2 5 ๐‘ฅ ) 5 ๐‘ฅ s e n c o s s e n
  • B โˆ’ ( 1 2 5 ๐‘ฅ ) s e n c o s
  • C โˆ’ 1 2 ( 1 2 5 ๐‘ฅ ) 5 ๐‘ฅ s e n c o s s e n
  • D 6 0 ( 1 2 5 ๐‘ฅ ) 5 ๐‘ฅ s e n c o s s e n
  • E โˆ’ 6 0 ( 1 2 5 ๐‘ฅ ) 5 ๐‘ฅ s e n c o s s e n

Q22:

Se ๐‘ฆ = 7 ๐‘ฅ 9 ๐‘ฅ t g , determine d d ๐‘ฆ ๐‘ฅ .

  • A 7 ๐‘ฅ 7 ๐‘ฅ โˆ’ 7 ๐‘ฅ 9 ๐‘ฅ s e c t g 2
  • B 7 ๐‘ฅ 7 ๐‘ฅ + 7 ๐‘ฅ 9 ๐‘ฅ s e c t g 2 2
  • C 7 7 ๐‘ฅ โˆ’ 7 ๐‘ฅ 9 ๐‘ฅ s e c t g 2 2
  • D 7 ๐‘ฅ 7 ๐‘ฅ โˆ’ 7 ๐‘ฅ 9 ๐‘ฅ s e c t g 2 2
  • E โˆ’ 7 ๐‘ฅ 7 ๐‘ฅ โˆ’ 7 ๐‘ฅ 9 ๐‘ฅ s e c t g 2 2

Q23:

Se ๐‘ฆ = 6 ๏€น 6 ๐‘ฅ โˆ’ 1 1 ๏… t g 2 , determine d d ๐‘ฆ ๐‘ฅ .

  • A 7 2 ๐‘ฅ ๏€น 6 ๐‘ฅ โˆ’ 1 1 ๏… s e c 2
  • B 6 ๏€น 6 ๐‘ฅ โˆ’ 1 1 ๏… s e c 2 2
  • C 7 2 ๏€น 6 ๐‘ฅ โˆ’ 1 1 ๏… s e c 2 2
  • D 7 2 ๐‘ฅ ๏€น 6 ๐‘ฅ โˆ’ 1 1 ๏… s e c 2 2
  • E โˆ’ 7 2 ๐‘ฅ ๏€น 6 ๐‘ฅ โˆ’ 1 1 ๏… s e c 2 2