Lesson Worksheet: Differentiation of Trigonometric Functions Mathematics • Higher Education

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

Q1:

Find the thirty-third derivative of 𝑓(π‘₯)=π‘₯sin.

  • A0
  • Bsinπ‘₯
  • Cβˆ’π‘₯cos
  • Dβˆ’π‘₯sin
  • Ecosπ‘₯

Q2:

If 𝑦=βˆ’2π‘₯+6ο€»π‘₯2+ο€»πœ‹4οŠͺsincos, find dd𝑦π‘₯.

  • Aβˆ’8π‘₯+3ο€»π‘₯2ο‡οŠ©cos
  • Bβˆ’8π‘₯+3ο€»π‘₯2ο‡οŠ«cos
  • Cβˆ’8π‘₯+3ο€»π‘₯2+12ο€»πœ‹4ο‡οŠ©sincos
  • Dβˆ’2π‘₯βˆ’ο€»π‘₯2+12ο€»πœ‹4ο‡οŠ©cossin
  • Eβˆ’8π‘₯+3ο€»π‘₯2+ο€»πœ‹4ο‡οŠ©cossin

Q3:

Given that 𝑦=10π‘₯βˆ’29π‘₯cos, determine dd𝑦π‘₯.

  • A10+189π‘₯cos
  • B10+189π‘₯sin
  • C10+29π‘₯sin
  • D10π‘₯+189π‘₯sin

Q4:

If 𝑦=(27π‘₯+27π‘₯)sincos, find dd𝑦π‘₯.

  • A56(7π‘₯+7π‘₯)sincos
  • B47π‘₯+47π‘₯sincos
  • C814π‘₯cos
  • D5614π‘₯cos

Q5:

Find the derivative of the function 𝐽(πœƒ)=π‘›πœƒtan.

  • A𝐽′(πœƒ)=2π‘›π‘›πœƒπ‘›πœƒsectan
  • B𝐽′(πœƒ)=2π‘›πœƒsec
  • C𝐽′(πœƒ)=2π‘›π‘›πœƒπ‘›πœƒcsctan
  • D𝐽′(πœƒ)=2π‘›πœƒπ‘›πœƒsectan
  • E𝐽′(πœƒ)=βˆ’2π‘›π‘›πœƒπ‘›πœƒcsctan

Q6:

If 𝑦=π‘₯5π‘₯sin, determine dd𝑦π‘₯.

  • A5π‘₯5π‘₯+5π‘₯5π‘₯οŠͺcossin
  • B25π‘₯5π‘₯οŠͺcos
  • Cβˆ’5π‘₯5π‘₯+5π‘₯5π‘₯οŠͺcossin
  • D5π‘₯+55π‘₯οŠͺcos
  • E5π‘₯5π‘₯βˆ’5π‘₯5π‘₯οŠͺcossin

Q7:

Given 𝑦=4π‘₯4π‘₯sintan, find dd𝑦π‘₯ at π‘₯=πœ‹6.

  • Aβˆ’6√3
  • Bβˆ’2+2√3
  • C10√3
  • D5√32

Q8:

Differentiate 𝑦=4π‘₯5βˆ’π‘₯tan.

  • A𝑦′=20βˆ’4π‘₯+4π‘₯π‘₯(5βˆ’π‘₯)tansectan
  • B𝑦′=20βˆ’4π‘₯+4π‘₯π‘₯(5βˆ’π‘₯)tansectan
  • C𝑦′=20βˆ’4π‘₯βˆ’4π‘₯π‘₯(5βˆ’π‘₯)tansectan
  • D𝑦′=20βˆ’4π‘₯+4π‘₯π‘₯5βˆ’π‘₯tansectan
  • E𝑦′=20βˆ’4π‘₯βˆ’4π‘₯π‘₯(5βˆ’π‘₯)tansectan

Q9:

Given that 𝑦=6π‘₯1βˆ’6π‘₯cossin, determine dd𝑦π‘₯ at π‘₯=πœ‹4.

  • Aβˆ’3
  • Bβˆ’14
  • C14
  • D3
  • E0

Q10:

Differentiate 𝑦=𝑑𝑑2+5𝑑sin.

  • A𝑦′=ο€Ή5𝑑+2𝑑𝑑+2𝑑(2+5𝑑)secsin
  • B𝑦′=ο€Ή5𝑑+2𝑑𝑑+2𝑑2+5π‘‘οŠ¨cossin
  • C𝑦′=ο€Ή5𝑑+2𝑑𝑑+2𝑑(2+5𝑑)cossin
  • D𝑦′=ο€Ή5𝑑+2π‘‘ο…π‘‘βˆ’2𝑑(2+5𝑑)cossin
  • E𝑦′=ο€Ήβˆ’5π‘‘βˆ’2𝑑𝑑+2𝑑(2+5𝑑)cossin

This lesson includes 96 additional questions and 896 additional question variations for subscribers.

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