Lesson Worksheet: Derivatives Mathematics

In this worksheet, we will practice using the rules of differentiation to find the derivative of a function.

Q1:

Find dd𝑦𝑥 if 𝑦=6𝑥7 .

  • A37𝑥
  • B37𝑥
  • C67𝑥
  • D3𝑥7

Q2:

Find the derivative of 𝑓(𝑥)=𝑥 by first principles.

Find the derivative of 𝑓(𝑥)=𝑥 by first principles.

  • A𝑥
  • B2
  • C2𝑥
  • D2𝑥
  • E2𝑥

Find the derivative of 𝑓(𝑥)=𝑥 by first principles.

  • A3𝑥
  • B3𝑥
  • C3𝑥
  • D𝑥
  • E3𝑥

By considering the pattern, what is the derivative of 𝑓(𝑥)=𝑥?

  • Add𝑥(𝑥)=𝑛𝑥
  • Bdd𝑥(𝑥)=𝑛𝑥
  • Cdd𝑥(𝑥)=𝑛𝑥
  • Ddd𝑥(𝑥)=𝑛𝑥
  • Edd𝑥(𝑥)=𝑥

Q3:

Find the derivative of 𝑓(𝑥)=𝑥.

  • A12𝑥
  • B12𝑥
  • C𝑥2
  • D2𝑥3
  • E1𝑥

Q4:

Find the derivative of 𝑓(𝑥)=𝑥.

  • A1𝑥
  • B1𝑥
  • C1
  • D1
  • E0

Q5:

Find dd𝑦𝑥, given that 𝑦=8𝑥4𝑥+3𝑥+5.

  • A72𝑥20𝑥+3
  • B72𝑥20𝑥+3
  • C8𝑥4𝑥+3
  • D72𝑥20𝑥

Q6:

Find dd𝑦𝑥, given that 𝑦=22𝑥.

  • A88𝑥
  • B88𝑥
  • C22𝑥
  • D88𝑥

Q7:

Find dd𝑦𝑥, given that 𝑦=7𝑥+1𝑥.

  • A35𝑥6𝑥
  • B35𝑥6𝑥
  • C35𝑥+6𝑥
  • D35𝑥6𝑥
  • E7𝑥+1𝑥

Q8:

Given that 𝑦=𝑥+𝑥+8𝑥 and 𝑧=𝑥(𝑥4)(𝑥1), determine dddd𝑦𝑥𝑧𝑥.

  • A4𝑥4
  • B12𝑥+4
  • C12𝑥+12
  • D2𝑥4
  • E8𝑥+4

Q9:

Differentiate the function 𝑓(𝑥)=𝑥73𝑥4.

  • A𝑓(𝑥)=𝑥73𝑥4𝑥
  • B𝑓(𝑥)=2𝑥73
  • C𝑓(𝑥)=𝑥73
  • D𝑓(𝑥)=2𝑥73𝑥4𝑥
  • E𝑓(𝑥)=2𝑥73𝑥4

Q10:

Given that 𝑓(𝑥)=𝑥+𝑚𝑥+1, determine 𝑚 if 𝑓(3)=1.

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