Learning pack · IGCSE handout

Differentiation

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Differentiation finds gradients of curves. For polynomials, differentiate term by term: $\frac{d}{dx}(ax^n)=anx^{n-1}$ .

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (1)📖 Full summary

Files: 49_differentiation_handout.pdf · 49_differentiation_handout_answers.pdf

Full topic summary

Differentiation finds gradients of curves. For polynomials, differentiate term by term: $\frac{d}{dx}(ax^n)=anx^{n-1}$ .

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

\frac{dy}{dx}=12x^3-2

Power rule.

Worked example 2 — Gradient at a point

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

Working

6

Differentiate, then substitute.

Worked example 3 — Stationary point

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

Working

x=2

Set derivative to zero.

🎬 Topic videos

Implicit differentiation, what's going on here? | Chapter 6, Essence of calculus
3Blue1Brown · 16 min
Classroom-ready explain of rates of change, functions. Use when teaching this topic in Lower Secondary / IGCSE.

More Lower Secondary packs

Browse the hub Learning Packs & Summary, or open the compact Differentiation summary.