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.

  • Acos3𝑥
  • B63𝑥cos
  • C183𝑥cos
  • D33𝑥cos
  • E183𝑥cos

Q2:

If 𝑦=72𝑥tan, find dd𝑦𝑥.

  • A142𝑥sec
  • B142𝑥sec
  • Csec2𝑥
  • D142𝑥sec
  • E72𝑥sec

Q3:

Given that 𝑦=10𝑥29𝑥cos, determine dd𝑦𝑥.

  • A10+189𝑥cos
  • B10+189𝑥sin
  • C10+29𝑥sin
  • D10𝑥+189𝑥sin

Q4:

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

  • A63
  • B2+23
  • C103
  • D532

Q5:

If 𝑦=64𝑥+22𝑥cossin, find dd𝑦𝑥.

  • A244𝑥42𝑥sincos
  • B64𝑥+42𝑥sincos
  • C244𝑥42𝑥cossin
  • D244𝑥+42𝑥sincos

Q6:

If 𝑦=𝑥5𝑥sin, determine dd𝑦𝑥.

  • A5𝑥5𝑥+5𝑥5𝑥cossin
  • B25𝑥5𝑥cos
  • C5𝑥5𝑥+5𝑥5𝑥cossin
  • D5𝑥+55𝑥cos
  • E5𝑥5𝑥5𝑥5𝑥cossin

Q7:

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

  • A𝑦
  • B2𝑦𝑥csc
  • C𝑦𝑥csc
  • D𝑦𝑥csc

Q8:

If 𝑦=7𝑥9𝑥tan, find dd𝑦𝑥.

  • A7𝑥7𝑥+7𝑥9𝑥sectan
  • B7𝑥7𝑥7𝑥9𝑥sectan
  • C7𝑥7𝑥7𝑥9𝑥sectan
  • D7𝑥7𝑥7𝑥9𝑥sectan
  • E77𝑥7𝑥9𝑥sectan

Q9:

If 𝑦=6𝑥16𝑥cossin, find dd𝑦𝑥.

  • A616𝑥sin
  • B616𝑥sin
  • C1(16𝑥)sin
  • D6(16𝑥)sin
  • E6𝑥(16𝑥)sinsin

Q10:

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

Q11:

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

  • A55𝑥𝜋7sec
  • B55𝑥𝜋7sec
  • C55𝑥+𝜋7sec
  • D55𝑥+𝜋7sec
  • Esec5𝑥+𝜋7

Q12:

If 𝑦=3(8𝑥3)cos, find dd𝑦𝑥.

  • A(8𝑥3)sin
  • B24(8𝑥3)sin
  • C24(8𝑥3)sin
  • D3(8𝑥3)sin
  • E8(8𝑥3)sin

Q13:

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

  • A6𝑥+4𝑥+24(6𝑥+1)sincoscos
  • B6𝑥4𝑥24(6𝑥+1)sincoscos
  • C2𝑥3𝑥cossin
  • D6𝑥+4𝑥+246𝑥+1sincoscos

Q14:

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

  • A53
  • B53
  • C5
  • D5

Q15:

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

  • A942𝑥3cos
  • B232𝑥3cos
  • C322𝑥3cos
  • D322𝑥3cos

Q16:

If 𝑦=72𝑥222𝑥sincos, find dd𝑦𝑥.

  • A72𝑥csc
  • B72𝑥sec
  • C72𝑥csc
  • D72𝑥sec

Q17:

Determine the derivative of 𝑓(𝑡)=𝑡5𝜋𝑡sin.

  • A𝑓(𝑡)=5𝜋𝑡5𝜋𝑡5𝜋𝑡cossin
  • B𝑓(𝑡)=5𝜋𝑡5𝜋𝑡+5𝜋𝑡cossin
  • C𝑓(𝑡)=5𝜋𝑡5𝜋𝑡+5𝜋𝑡cossin
  • D𝑓(𝑡)=𝑡(5𝜋𝑡+5𝜋𝑡)sincos

Q18:

Differentiate 2𝑥132𝑥+3coscos.

  • A22𝑥32𝑥cossin
  • B2𝑥𝑥cossin
  • C13
  • D2𝑥3𝑥cossin

Q19:

Find dd𝑦𝑥, given that 𝑦=8𝑥𝑥66𝑥2cossin.

  • A4𝑥3𝑥68𝑥63𝑥2cossinsin
  • B4𝑥3𝑥68𝑥63𝑥2sincoscos
  • C4𝑥3𝑥68𝑥6+3𝑥2sincoscos
  • D4𝑥3𝑥63𝑥2sincos
  • E𝑥𝑥68𝑥6+𝑥2cossinsin

Q20:

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

  • A3𝜋
  • B4
  • C4
  • D3𝜋

Q21:

If 𝑦=8𝑥6𝑥cos, find dd𝑦𝑥.

  • A48𝑥6𝑥+86𝑥sincos
  • B48𝑥6𝑥86𝑥sincos
  • C48𝑥6𝑥+86𝑥sincos
  • D8𝑥6𝑥86𝑥sincos

Q22:

Find the derivative of the function 𝐽(𝜃)=𝑛𝜃tan.

  • A𝐽(𝜃)=2𝑛𝑛𝜃𝑛𝜃sectan
  • B𝐽(𝜃)=2𝑛𝜃sec
  • C𝐽(𝜃)=2𝑛𝑛𝜃𝑛𝜃csctan
  • D𝐽(𝜃)=2𝑛𝜃𝑛𝜃sectan
  • E𝐽(𝜃)=2𝑛𝑛𝜃𝑛𝜃csctan

Q23:

Evaluate the rate of change of 𝑓(𝑥)=5𝑥tan at 𝑥=𝜋.

Q24:

If 𝑦=𝜋6+57𝑥sinsin, find dd𝑦𝑥.

  • A77𝑥cos
  • B357𝑥cos
  • C357𝑥cos
  • Dsincos𝜋6+357𝑥

Q25:

If 𝑦=2𝑥+3𝑥sin, find dd𝑦𝑥.

  • A2+33𝑥cos
  • B233𝑥cos
  • C2+33𝑥sin
  • D2+3𝑥cos

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