Glossary

Differentiation – Key Terms & Definitions

Q: How many differentiation terms do I need to know for IGCSE?

This glossary covers 12 key differentiation terms. Focus on understanding definitions and being able to use each term in context during exams.

Q: Are these terms for Core or Extended?

Terms are labelled as Core or Extended. Core students should focus on Core-labelled terms, while Extended students need to know all terms.

Essential differentiation vocabulary for IGCSE Mathematics (0580). Each term includes a clear definition and example to help you understand and remember key concepts.

derivative

Extended

Rate of change of a function

Example

$\dfrac{dy}{dx} \text{ of } x^2 \text{ is } 2x$

gradient of curve

Extended

Slope at a specific point

Example

$\dfrac{dy}{dx} \text{ evaluated at } x = a$

tangent

Extended

Line touching curve at one point

Example

Has same gradient as curve there

stationary point

Extended

Where gradient equals zero

Example

$\dfrac{dy}{dx} = 0$

maximum

Extended

Highest point locally

Example

$\dfrac{d^2y}{dx^2} < 0 \text{ at maximum}$

minimum

Extended

Lowest point locally

Example

$\dfrac{d^2y}{dx^2} > 0 \text{ at minimum}$

turning point

Extended

Where curve changes direction

Example

Maximum or minimum point

increasing function

Extended

Gradient is positive

Example

$\dfrac{dy}{dx} > 0$

decreasing function

Extended

Gradient is negative

Example

$\dfrac{dy}{dx} < 0$

second derivative

Extended

Derivative of the derivative

Example

$\dfrac{d^2y}{dx^2} \text{ tests nature of stationary point}$

rate of change

Extended

How quickly one quantity changes relative to another

Example

Speed is rate of change of distance

power rule

Extended

$\text{Differentiate } x^n \text{ to get } nx^{n-1}$

Example

$\dfrac{d}{dx}(x^3) = 3x^2$

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Frequently Asked Questions

How many differentiation terms do I need to know for IGCSE?

This glossary covers 12 key differentiation terms. Focus on understanding definitions and being able to use each term in context during exams.

Are these terms for Core or Extended?

Terms are labelled as Core or Extended. Core students should focus on Core-labelled terms, while Extended students need to know all terms.

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