Differentiation

What the lesson covers

• The gradient of a curve
• First principles: deriving the rule
• Differentiating in practice: rewrite first
• Rates of change and the second derivative
• Tangents and normals
• Stationary points and the shape of a curve
• Optimisation
• Strategy and intuitive checks
• Self-check questions with answers (8)

Specification: MM6.1-6.3. Codes follow the UAT-UK ESAT content specification.

How to use it

1. Read a section, then cover the worked example and try it yourself.
2. Check the common mistakes list: these are the slips the real test is built to catch.
3. Do the self-check without looking back. Mark it against the answers.
4. Then practise the topic under time, with the matching practice set.