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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

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Derivative - IGCSE Maths Definition

What is a derivative in IGCSE maths?

Derivatives revision resources to ace your exams

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Reviewer: Amber

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