Differentiation summary

Key learning points

• Gradient function $\frac{dy}{dx}$; stationary points where $\frac{dy}{dx}=0$.
• Second derivative test: $\frac{d^2y}{dx^2}>0$ local min; $<0$ local max.
• Tangents and normals use the gradient at a point.

Worked example 1 — Differentiate

Differentiate $y=3x^4-2x$.

Working

Power rule.

Worked example 2 — Gradient at a point

$y=x^2$ at $x=3$. Gradient?

Working

Differentiate, then substitute.

Worked example 3 — Stationary point

$y=x^2-4x+1$. Stationary $x$?

Working

Set derivative to zero.

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.