Cambridge AS & A Level Mathematics
1.7Differentiation
Differentiation in Cambridge AS & A Level Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
Topic71 practice questions4 lessons
Learning objectives
What the syllabus expects you to be able to do.
- 1.7.1Understand the gradient of a curve as the limit of gradients of chords, and use the derivative notations.
- 1.7.2Differentiate xⁿ for rational n, with constant multiples, sums, differences and composites (chain rule).
- 1.7.3Apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change.
- 1.7.4Locate stationary points, determine their nature and use them in sketching graphs.
Lessons
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Differentiating powers of x and the chain rule
40 min
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Stationary points, optimisation and curve sketching
50 min
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Tangents, normals, increasing functions and rates of change
45 min
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The gradient of a curve and differentiation from first principles
40 min
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Sample question
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