Worksheet: Differentiation of Trigonometric Functions

In this worksheet, we will practice finding the derivatives of trigonometric functions and applying the differentiation rules on them.

Q1:

Find dd𝑦𝑥, given that 𝑦=63𝑥sin.

  • A c o s 3 𝑥
  • B 6 3 𝑥 c o s
  • C 1 8 3 𝑥 c o s
  • D 3 3 𝑥 c o s
  • E 1 8 3 𝑥 c o s

Q2:

If 𝑦=72𝑥tan, find dd𝑦𝑥.

  • A 1 4 2 𝑥 s e c
  • B 1 4 2 𝑥 s e c
  • C s e c 2 𝑥
  • D 1 4 2 𝑥 s e c
  • E 7 2 𝑥 s e c

Q3:

Given that 𝑦=10𝑥29𝑥cos, determine dd𝑦𝑥.

  • A 1 0 + 1 8 9 𝑥 c o s
  • B 1 0 + 1 8 9 𝑥 s i n
  • C 1 0 + 2 9 𝑥 s i n
  • D 1 0 𝑥 + 1 8 9 𝑥 s i n

Q4:

If 𝑦=2(3+8𝑥)sin, determine dd𝑦𝑥.

  • A 1 6 ( 3 + 8 𝑥 ) c o s
  • B c o s ( 3 + 8 𝑥 )
  • C 2 ( 3 + 8 𝑥 ) c o s
  • D 8 ( 3 + 8 𝑥 ) c o s
  • E 1 6 ( 3 + 8 𝑥 ) c o s

Q5:

Given 𝑦=4𝑥4𝑥sintan, find dd𝑦𝑥 at 𝑥=𝜋6.

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

Q6:

If 𝑦=64𝑥+22𝑥cossin, find dd𝑦𝑥.

  • A 2 4 4 𝑥 4 2 𝑥 s i n c o s
  • B 6 4 𝑥 + 4 2 𝑥 s i n c o s
  • C 2 4 4 𝑥 4 2 𝑥 c o s s i n
  • D 2 4 4 𝑥 + 4 2 𝑥 s i n c o s

Q7:

If 𝑦=(4𝑥8)+(8𝑥+6)sincos, find dd𝑦𝑥.

  • A 8 ( 8 𝑥 + 6 ) 4 ( 4 𝑥 8 ) s i n c o s
  • B 8 ( 8 𝑥 + 6 ) + 4 ( 4 𝑥 8 ) s i n c o s
  • C ( 8 𝑥 + 6 ) ( 4 𝑥 8 ) s i n c o s
  • D 4 ( 4 𝑥 8 ) 8 ( 8 𝑥 + 6 ) s i n c o s

Q8:

If 𝑦=𝑥5𝑥sin, determine dd𝑦𝑥.

  • A 5 𝑥 5 𝑥 + 5 𝑥 5 𝑥 c o s s i n
  • B 2 5 𝑥 5 𝑥 c o s
  • C 5 𝑥 5 𝑥 + 5 𝑥 5 𝑥 c o s s i n
  • D 5 𝑥 + 5 5 𝑥 c o s
  • E 5 𝑥 5 𝑥 5 𝑥 5 𝑥 c o s s i n

Q9:

If 𝑦=7𝑥(5𝑥+4)sin, find dd𝑦𝑥.

  • A 7 𝑥 ( 5 𝑥 + 4 ) + 7 ( 5 𝑥 + 4 ) c o s s i n
  • B 5 ( 5 𝑥 + 4 ) + 7 c o s
  • C 5 𝑥 ( 5 𝑥 + 4 ) + 7 ( 5 𝑥 + 4 ) c o s s i n
  • D 3 5 𝑥 ( 5 𝑥 + 4 ) + 7 ( 5 𝑥 + 4 ) c o s s i n
  • E 3 5 𝑥 ( 5 𝑥 + 4 ) + 7 ( 5 𝑥 + 4 ) c o s s i n

Q10:

If 𝑦=𝑥1𝑥sincos, which of the following is the same as 𝑦?

  • A 𝑦
  • B 2 𝑦 𝑥 c s c
  • C 𝑦 𝑥 c s c
  • D 𝑦 𝑥 c s c

Q11:

If 𝑦=7𝑥9𝑥tan, find dd𝑦𝑥.

  • A 7 𝑥 7 𝑥 + 7 𝑥 9 𝑥 s e c t a n
  • B 7 𝑥 7 𝑥 7 𝑥 9 𝑥 s e c t a n
  • C 7 𝑥 7 𝑥 7 𝑥 9 𝑥 s e c t a n
  • D 7 𝑥 7 𝑥 7 𝑥 9 𝑥 s e c t a n
  • E 7 7 𝑥 7 𝑥 9 𝑥 s e c t a n

Q12:

If 𝑦=6𝑥16𝑥cossin, find dd𝑦𝑥.

  • A 6 1 6 𝑥 s i n
  • B 6 1 6 𝑥 s i n
  • C 1 ( 1 6 𝑥 ) s i n
  • D 6 ( 1 6 𝑥 ) s i n
  • E 6 𝑥 ( 1 6 𝑥 ) s i n s i n

Q13:

Given that 𝑦=(2𝑥7)(8𝑥+19)cossin, determine dd𝑦𝑥 at 𝑥=𝜋.

Q14:

Given that 𝑦=5𝑥+15𝑥tantantantan, determine dd𝑦𝑥.

  • A 5 5 𝑥 𝜋 7 s e c
  • B 5 5 𝑥 𝜋 7 s e c
  • C 5 5 𝑥 + 𝜋 7 s e c
  • D 5 5 𝑥 + 𝜋 7 s e c
  • E s e c 5 𝑥 + 𝜋 7

Q15:

Find the first derivative of the function 𝑦=2(9𝑥4)(9𝑥4)sincos.

  • A 2 ( 1 8 𝑥 8 ) s i n
  • B 2 ( 1 8 𝑥 8 ) s i n
  • C 1 8 ( 1 8 𝑥 8 ) c o s
  • D 1 8 ( 1 8 𝑥 8 ) c o s

Q16:

If 𝑦=3(8𝑥3)cos, find dd𝑦𝑥.

  • A ( 8 𝑥 3 ) s i n
  • B 2 4 ( 8 𝑥 3 ) s i n
  • C 2 4 ( 8 𝑥 3 ) s i n
  • D 3 ( 8 𝑥 3 ) s i n
  • E 8 ( 8 𝑥 3 ) s i n

Q17:

Find the first derivative of the function 𝑦=4𝑥+16𝑥+1sincos.

  • A 6 𝑥 + 4 𝑥 + 2 4 ( 6 𝑥 + 1 ) s i n c o s c o s
  • B 6 𝑥 4 𝑥 2 4 ( 6 𝑥 + 1 ) s i n c o s c o s
  • C 2 𝑥 3 𝑥 c o s s i n
  • D 6 𝑥 + 4 𝑥 + 2 4 6 𝑥 + 1 s i n c o s c o s

Q18:

If 𝑦=2𝑥+3𝑥2𝑥2𝑥sincossincos, find dd𝑦𝑥 at 𝑥=7𝜋12.

  • A 5 3
  • B 5 3
  • C 5
  • D5

Q19:

Find the first derivative of the function 𝑦=9𝑥3𝑥6𝑥6coscossin.

  • A 9 4 2 𝑥 3 c o s
  • B 2 3 2 𝑥 3 c o s
  • C 3 2 2 𝑥 3 c o s
  • D 3 2 2 𝑥 3 c o s

Q20:

If 𝑦=72𝑥222𝑥sincos, find dd𝑦𝑥.

  • A 7 2 𝑥 c s c
  • B 7 2 𝑥 s e c
  • C 7 2 𝑥 c s c
  • D 7 2 𝑥 s e c

Q21:

Determine the derivative of 𝑓(𝑡)=𝑡5𝜋𝑡sin.

  • A 𝑓 ( 𝑡 ) = 5 𝜋 𝑡 5 𝜋 𝑡 5 𝜋 𝑡 c o s s i n
  • B 𝑓 ( 𝑡 ) = 5 𝜋 𝑡 5 𝜋 𝑡 + 5 𝜋 𝑡 c o s s i n
  • C 𝑓 ( 𝑡 ) = 5 𝜋 𝑡 5 𝜋 𝑡 + 5 𝜋 𝑡 c o s s i n
  • D 𝑓 ( 𝑡 ) = 𝑡 ( 5 𝜋 𝑡 + 5 𝜋 𝑡 ) s i n c o s

Q22:

Differentiate 2𝑥132𝑥+3coscos.

  • A 2 2 𝑥 3 2 𝑥 c o s s i n
  • B 2 𝑥 𝑥 c o s s i n
  • C 1 3
  • D 2 𝑥 3 𝑥 c o s s i n

Q23:

Find dd𝑦𝑥, given that 𝑦=8𝑥𝑥66𝑥2cossin.

  • A 4 𝑥 3 𝑥 6 8 𝑥 6 3 𝑥 2 c o s s i n s i n
  • B 4 𝑥 3 𝑥 6 8 𝑥 6 3 𝑥 2 s i n c o s c o s
  • C 4 𝑥 3 𝑥 6 8 𝑥 6 + 3 𝑥 2 s i n c o s c o s
  • D 4 𝑥 3 𝑥 6 3 𝑥 2 s i n c o s
  • E 𝑥 𝑥 6 8 𝑥 6 + 𝑥 2 c o s s i n s i n

Q24:

Given that 𝑦=(4𝑥9)𝜋𝑥3cos, determine dd𝑦𝑥 at 𝑥=0.

  • A 3 𝜋
  • B4
  • C 4
  • D 3 𝜋

Q25:

If 𝑦=8𝑥6𝑥cos, find dd𝑦𝑥.

  • A 4 8 𝑥 6 𝑥 + 8 6 𝑥 s i n c o s
  • B 4 8 𝑥 6 𝑥 8 6 𝑥 s i n c o s
  • C 4 8 𝑥 6 𝑥 + 8 6 𝑥 s i n c o s
  • D 8 𝑥 6 𝑥 8 6 𝑥 s i n c o s

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