Full Differentiation Notes — Cambridge IGCSE Additional Mathematics 0606

Topic 14: Calculus, differentiation section. Built from the 2025–2027 Cambridge IGCSE Additional Mathematics 0606 syllabus.

What this chapter must train

By the end, students should be able to:

• Understand the idea of a derived function.
• Use derivative notation correctly.
• Differentiate standard functions.
• Use the chain rule.
• Differentiate products and quotients.
• Find gradients, tangents, and normals.
• Find stationary points.
• Use first and second derivative tests.
• Apply differentiation to rates of change, small increments, maxima and minima.

1. What differentiation means

Differentiation finds the gradient of a curve at a point.

For a straight line, the gradient is constant.

For a curve, the gradient changes from point to point.

The derivative gives the gradient function.

If: