What is differentiation? | Maths Tutorials from an Oxford Graduate

Learn what differentiation really is with an Oxford graduate. This lesson is an introduction to differentiation and explains what it is we are actually finding when we differentiate.

Differentiation is all about rate of change or gradient. In order to understand this, we look at a simple example (y=x^2) and derive the equation for the gradient from first principles. At each step, we talk about exactly what we are doing and what it all means - something that is often lost in the teaching and learning of differentiation. Understanding this will help you appreciate what the standard results table is all about.

This is the first lesson in a series on differentiation. It introduces the concept of differentiation but does not actually explain in depth how to differentiate anything other than y=x^2. For how to actually differentiate, click on the following links:
1. How to differentiate powers of x using the power rule:    • Power Rule for Differentiation | How ...  
2. How to differentiate other common functions: (coming very soon)
3. How to use the chain rule: (coming very soon)
4. How to use the product rule: (coming very soon)
5. How to use the quotient rule: (coming very soon)
6. How to do successive differentiation: (coming soon)
7. How to use differentiation to find maximum and minimum points: (coming soon)
8. How to do logarithmic differentiation: (coming soon)
9. How to differentiate more complex functions: (coming soon)

If you want to watch a specific part of the lesson, click on the following links to take you to the relevant part of the video:
- What differentiation is all about: 01:04
- An example - y=x^2 : 04:06
- What the derivative really means: 10:54
- An introduction to standard results: 12:48

Previous knowledge required:
- An understanding of gradient: (coming soon)
- How to transpose equations: (coming soon)
- How to simplify algebra: (coming soon)
- An understanding of graphs

Where to go next:
- How to do and use differentiation (see list above)
- An introduction to integration: (coming soon)
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