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 d d 𝑦 𝑥 , given that 𝑦 = 6 3 𝑥 s i n .

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

Q2:

If 𝑦 = 7 2 𝑥 t a n , find d d 𝑦 𝑥 .

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

Q3:

Given that 𝑦 = 1 0 𝑥 2 9 𝑥 c o s , determine d d 𝑦 𝑥 .

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

Q4:

If 𝑦 = 2 ( 3 + 8 𝑥 ) s i n , determine d d 𝑦 𝑥 .

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

Q5:

Given 𝑦 = 4 𝑥 4 𝑥 s i n t a n , find d d 𝑦 𝑥 at 𝑥 = 𝜋 6 .

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

Q6:

If 𝑦 = 6 4 𝑥 + 2 2 𝑥 c o s s i n , find d d 𝑦 𝑥 .

  • A 6 4 𝑥 + 4 2 𝑥 s i n c o s
  • B 2 4 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 = ( 4 𝑥 8 ) + ( 8 𝑥 + 6 ) s i n c o s , find d d 𝑦 𝑥 .

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

Q8:

If 𝑦 = 𝑥 5 𝑥 5 s i n , determine d d 𝑦 𝑥 .

  • A 5 𝑥 5 𝑥 + 5 𝑥 5 𝑥 5 4 c o s s i n
  • B 5 𝑥 + 5 5 𝑥 4 c o s
  • C 5 𝑥 5 𝑥 5 𝑥 5 𝑥 5 4 c o s s i n
  • D 5 𝑥 5 𝑥 + 5 𝑥 5 𝑥 5 4 c o s s i n
  • E 2 5 𝑥 5 𝑥 4 c o s

Q9:

If 𝑦 = 7 𝑥 ( 5 𝑥 + 4 ) s i n , find d d 𝑦 𝑥 .

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

Q10:

If 𝑦 = 𝑥 1 𝑥 s i n c o s , which of the following is the same as 𝑦 ?

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

Q11:

If 𝑦 = 7 𝑥 9 𝑥 t a n , find d d 𝑦 𝑥 .

  • A 7 𝑥 7 𝑥 7 𝑥 9 𝑥 s e c t a n 2
  • B 7 𝑥 7 𝑥 + 7 𝑥 9 𝑥 s e c t a n 2 2
  • C 7 7 𝑥 7 𝑥 9 𝑥 s e c t a n 2 2
  • D 7 𝑥 7 𝑥 7 𝑥 9 𝑥 s e c t a n 2 2
  • E 7 𝑥 7 𝑥 7 𝑥 9 𝑥 s e c t a n 2 2

Q12:

If 𝑦 = 6 𝑥 1 6 𝑥 c o s s i n , find d d 𝑦 𝑥 .

  • A 6 ( 1 6 𝑥 ) s i n 2
  • B 6 1 6 𝑥 s i n
  • C 1 ( 1 6 𝑥 ) s i n 2
  • D 6 1 6 𝑥 s i n
  • E 6 𝑥 ( 1 6 𝑥 ) s i n s i n 2

Q13:

Given that 𝑦 = ( 2 𝑥 7 ) ( 8 𝑥 + 1 9 ) c o s s i n , determine d d 𝑦 𝑥 at 𝑥 = 𝜋 .

Q14:

Given that 𝑦 = 5 𝑥 + 1 5 𝑥 t a n t a n t a n t a n 𝜋 7 𝜋 7 , determine d d 𝑦 𝑥 .

  • A s e c 2 5 𝑥 + 𝜋 7
  • B 5 5 𝑥 𝜋 7 s e c 2
  • C 5 5 𝑥 + 𝜋 7 s e c
  • D 5 5 𝑥 + 𝜋 7 s e c 2
  • E 5 5 𝑥 𝜋 7 s e c

Q15:

Find the first derivative of the function 𝑦 = 2 ( 9 𝑥 4 ) ( 9 𝑥 4 ) s i n c o s .

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

Q16:

If 𝑦 = 3 ( 8 𝑥 3 ) c o s , find d d 𝑦 𝑥 .

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

Q17:

Find the first derivative of the function 𝑦 = 4 𝑥 + 1 6 𝑥 + 1 s i n c o s .

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

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