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 |
---|---|---|---|

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 |

G Differentiation | G5 Parametric and Implicit 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 |