GlossariesIGCSE GlossariesIGCSE Maths GlossaryDerivative

Derivative - IGCSE Maths Definition

Reviewed by: Amber

Last updated

5 March 2025

What is a derivative in IGCSE maths?

In IGCSE maths, a derivative is a mathematical expression that represents the rate of change of a function.

The derivative is also known as the gradient function and represents the gradient (or slope) of the function's graph at a particular point.

The derivative is written as $\frac{d y}{d x}$

The general definition of a derivative is:

For a function in the form of a power of $x$ :

$y = a x^{n}$

the derivative is:

$\frac{d y}{d x} = n a x^{n - 1}$

For example:

If $y = 2 x^{3}$ then $\frac{d y}{d x} = 3 \times 2 x^{3 - 1} = 6 x^{2}$
If $y = x^{2}$ then $\frac{d y}{d x} = 2 \times x^{2 - 1} = 2 x$
If $y = 6 x$ then $\frac{d y}{d x} = 1 \times 6 x^{1 - 1} = 6 x^{0} = 6$
If $y = 2 x^{3} + x^{2} - 6 x$ then $\frac{d y}{d x} = 6 x^{2} + 2 x - 6$

Derivatives revision resources to ace your exams

You can find out more about derivatives and how they can be used, by reading our revision notes. To test your knowledge, try our exam questions in the differentiation section.

For quick-fire IGCSE maths revision, use our collection of interactive flashcards for IGCSE maths. We also have past papers for your exam practice.

Explore our IGCSE maths revision resources

Examiner-written IGCSE Maths revision resources that improve your grades 2x

Written by expert teachers and examiners
Aligned to exam specifications
Everything you need to know, and nothing you don’t

IGCSE Maths revision resources

Related IGCSE Maths glossary terms

Arithmetic Sequence: IGCSE Maths Definition
Amber, Maths Content Creator

Share this article

Derivative - IGCSE Maths Definition

What is a derivative in IGCSE maths?

Derivatives revision resources to ace your exams

Reviewer: Amber

The examiner written revision resources that improve your grades 2x.