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.
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.
This question appears in the following syllabi:
| Syllabus | Module | Section | Topic | Exam Year |
|---|---|---|---|---|
| AP Calculus BC (USA) | 3 | Differentiation | Parametric differentiation | - |
| AQA A-Level (UK - Pre-2017) | C4 | Differentiation | Parametric differentiation | - |
| AQA A2 Maths 2017 | Pure Maths | Parametric Equations | Parametric Differentiation | - |
| AQA AS/A2 Maths 2017 | Pure Maths | Parametric Equations | Parametric Differentiation | - |
| CBSE XII (India) | Calculus | Continuity and Differentiability | Derivatives of parametric functions | - |
| CCEA A-Level (NI) | C4 | Differentiation | Parametric differentiation | - |
| CIE A-Level (UK) | P2 | Differentiation | Parametric differentiation | - |
| Edexcel A-Level (UK - Pre-2017) | C4 | Differentiation | Parametric differentiation | - |
| Edexcel A2 Maths 2017 | Pure Maths | Differentiation | Parametric Differentiation | - |
| Edexcel AS/A2 Maths 2017 | Pure Maths | Differentiation | Parametric Differentiation | - |
| Methods (UK) | M8 | Differentiation | Parametric differentiation | - |
| OCR A-Level (UK - Pre-2017) | C4 | Differentiation | Parametric differentiation | - |
| OCR A2 Maths 2017 | Pure Maths | Differentiation Techniques | Parametric Differentiation | - |
| OCR MEI A2 Maths 2017 | Pure Maths | Parametric Equations | Parametric Differentiation | - |
| OCR-MEI A-Level (UK - Pre-2017) | C4 | Differentiation | Parametric differentiation | - |
| Pre-U A-Level (UK) | 4 | Differentiation | Parametric differentiation | - |
| Scottish Advanced Highers | M2 | Differentiation | Parametric differentiation | - |
| Scottish (Highers + Advanced) | AM2 | Differentiation | Parametric differentiation | - |
| Universal (all site questions) | D | Differentiation | Parametric differentiation | - |
| WJEC A-Level (Wales) | C4 | Differentiation | Parametric differentiation | - |