Differentiation (P4) Topic Review summary

Key learning points

• Differentiate powers, sums, and constant multiples fluently.
• Product, quotient, and chain rules as required by the module.
• Stationary points and second-derivative / sign tests.
• Tangents, normals, and connected rates of change.
• Implicit / parametric differentiation when the module includes them.

Worked example 1 — Power

Differentiate $5x^3$.

Working

$nx^{n-1}$.

Worked example 2 — Chain

Differentiate $(3x+1)^4$.

Working

Multiply by inner derivative 3.

Worked example 3 — Differentiate powers, sums, and constant m

Apply this idea from the Topic Review: Differentiate powers, sums, and constant multiples fluently.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Product, quotient, and chain rules as requ

Apply this idea from the Topic Review: Product, quotient, and chain rules as required by the module.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.