Differentiation

Rules and applications of differentiation, including derivatives of common functions, composite and implicit differentiation, tangents and normals, stationary points, concavity, limits, related rates and optimisation.

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Limits and Derivatives

Differentiation

The basic idea of a limit \(\lim_{x\to a}f(x)\) from tables and graphs, slope as a limit, rate of change and gradient, using the derivative definition \(f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}\), derivatives of \(x^n\), and linearity for sums and scalar multiples.

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Differentiation rules

Differentiation

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Tangents and normals

Differentiation

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Applications of the First Derivative

Differentiation

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Second Derivatives and Applications

Differentiation

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Implicit differentiation

Differentiation

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Related Rates

Differentiation

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n^th Derivative

Differentiation

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L'Hôpital's rule

Differentiation

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Differentiation

Rules and applications of differentiation, including derivatives of common functions, composite and implicit differentiation, tangents and normals, stationary points, concavity, limits, related rates and optimisation.