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If y is given as a function of a parameter t, and x is given as a function of the same parameter t, then \displaystyle \frac{dy}{dx} can be found by using: \displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} } = \frac{dy}{dt} \times \frac{dt}{dx}
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Glossary

function

A rule that connects one value in one set with one and only one value in another set.

parameter

a) a constant or variable term in a function that determines the specific form of the function but not its general nature, as a in f(x) = ax, where a determines only the slope of the line described by f(x).
b) one of the independent variables in a set of parametric equations.

union

The union of two sets A and B is the set containing all the elements of A and B.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopic
AP Calculus BC (USA)3DifferentiationParametric differentiation
AQA A-Level (UK - Pre-2017)C4DifferentiationParametric differentiation
AQA A2 Maths 2017Pure MathsParametric EquationsParametric Differentiation
AQA AS/A2 Maths 2017Pure MathsParametric EquationsParametric Differentiation
CBSE XII (India)CalculusContinuity and DifferentiabilityDerivatives of parametric functions
CCEA A-Level (NI)C4DifferentiationParametric differentiation
CIE A-Level (UK)P2DifferentiationParametric differentiation
G DifferentiationG5 Parametric and Implicit DifferentiationParametric Differentiation
Edexcel A-Level (UK - Pre-2017)C4DifferentiationParametric differentiation
Edexcel A2 Maths 2017Pure MathsDifferentiationParametric Differentiation
Edexcel AS/A2 Maths 2017Pure MathsDifferentiationParametric Differentiation
Methods (UK)M8DifferentiationParametric differentiation
OCR A-Level (UK - Pre-2017)C4DifferentiationParametric differentiation
OCR A2 Maths 2017Pure MathsDifferentiation TechniquesParametric Differentiation
OCR MEI A2 Maths 2017Pure MathsParametric EquationsParametric Differentiation
OCR-MEI A-Level (UK - Pre-2017)C4DifferentiationParametric differentiation
Pre-U A-Level (UK)4DifferentiationParametric differentiation
Scottish Advanced HighersM2DifferentiationParametric differentiation
Scottish (Highers + Advanced)AM2DifferentiationParametric differentiation
Universal (all site questions)DDifferentiationParametric differentiation
WJEC A-Level (Wales)C4DifferentiationParametric differentiation