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​
0. Unit Map
6. Interpreting Derivatives
7. Differentiating Simple Trigonometric, Exponential and Logarithmic Functions
10. Concativity and Points of Inflection
16. Further Exponentials and Logarithms
17. Further Trigonometric Functions
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