← Lesson📄 Worksheet✅ Memo📝 Exam test🗝️ Marking guide
∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 12 · Calculus
Differentiation: The Rules and How Exams Use Them
WORKSHEET
Name: 
Class: 
Date: 
Mark
  / 37

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Differentiate y = x4. (power rule)
    (1)
  2. 2
    Differentiate y = 5x3 − 2x2 + 7. (polynomial)
    (2)
  3. 3
    Differentiate y = 2x2 − 3x + 9. (polynomial)
    (2)
  4. 4
    Differentiate y = 3/x (write as 3x−1). (rewrite)
    (2)
  5. 5
    Differentiate y = √x (write as x^1/2). (rewrite)
    (2)
  6. 6
    From first principles, differentiate f(x) = 3x. (first principles)
    (4)
  7. 7
    Gradient of y = x2 + 2x at x = 1. (gradient)
    (2)
  8. 8
    Gradient of y = x3 at x = 2. (gradient)
    (2)
  9. 9
    Find x where y = x2 − 6x has a turning point. (turning point)
    (2)
  10. 10
    Find the turning points of y = x3 − 12x. (turning point)
    (4)
  11. 11
    Determine f′(x) from first principles if f(x) = 2x² − 3x.
    (5)
  12. 12
    Determine f′(x) from first principles if f(x) = 3/x.
    (5)
  13. 13
    Use first principles to show that the derivative of f(x) = 7 is 0.
    (2)
  14. 14
    Explain why you may NOT substitute h = 0 at the start of a first-principles question.
    (2)
TOTAL: 37 marks
© Danemathics — free to print and share for classroom use.danemathics.com

Printing this sheet

  1. In the print dialog open More settings and untick “Headers and footers” — that is what prints the date, time and web address in the margin.
  2. Leave Pages per sheet on 1 so learners keep the full writing space.
  3. Choose Save as PDF as the destination to download it instead of printing.