Unit 6 - Differential Calculus

Unit Objectives
Prior Knowledge:
  •  Laws of Indices
By the end of this unit students should be able to:
  • Understand limits, continuity and convergence
  • Know and use the definition of derivative from first principles
  • Understand derivatives as gradient functions and as rate of change
  • Find equations of tangents and normals
  • Identify increasing and decreasing functions
  • Find and interpret higher derivatives
  • Differentiate polynomials, trigonometric functions and their inverses and exponential and log functions
  • Differentiate using the chain, product and quotient rules
  • Differentiate implicitly
  • Solve problems of connected rates of change
  • Find and determine the nature of stationary points
  • Find points of inflection with zero and non-zero gradients
  • Solve problems of graphical behaviour of functions and the relationship between a function and its first and second derivatives.
Lesson Resources​
1. Limits and Continuity
2. Asymptotes and Algebraic Limits
3. First Principles and Differentiability
4. Differentiating Polynomials
5. Tangents and Normals
6. Stationary Points, Increasing and Decreasing Functions
7. ​Chain Rule
8. Product Rule
9. Quotient Rule
10. Higher Derivatives
11. Concativity and Points of Inflection
12. Graphical Relationship between f, f' and f''
13. Differentiating Exponentials and Logarithms
14. Differentiating Trigonometric Functions
15. Implicit Differentiation
16. Related Rates of Change
17. Optimisation
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