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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Concepts

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Limits and Derivatives

Differentiation

The basic idea of a limit x→alimf(x) from tables and graphs, slope as a limit, rate of change and gradient, using the derivative definition f′(x)=h→0limhf(x+h)−f(x), derivatives of xn, and linearity for sums and scalar multiples.

0/5 key exercises

Differentiation rules

Differentiation

0/5 key exercises

Tangents and normals

Differentiation

0/4 key exercises

Applications of the First Derivative

Differentiation

0/3 key exercises

Second Derivatives and Applications

Differentiation

0/4 key exercises

Implicit differentiation

Differentiation

0/2 key exercises

Related Rates

Differentiation

0/2 key exercises

n^th Derivative

Differentiation

0/1 key exercises

L'Hôpital's rule

Differentiation

0/0 key exercises

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.

Sign up to view your learning progress

Sign up

Choose a concept to study or jump straight into the problem bank.

Concepts

Start Here

Limits and Derivatives

Differentiation

The basic idea of a limit x→alimf(x) from tables and graphs, slope as a limit, rate of change and gradient, using the derivative definition f′(x)=h→0limhf(x+h)−f(x), derivatives of xn, and linearity for sums and scalar multiples.