This display allows you to investigate the first and second derivatives of some composite functions.

Select composite function:

## Summary/Background

A
note about graphic calculators1st and 2nd derivatives can be displayed on your graphic calculator, for example, on the TI-83: Select the Y= screen:Enter Y1 = Xsin(X)Y2 = nDerive(Y1,X,X)Y3 = nDerive(Y2,X,X)Then select the GRAPH screen. |

## Software/Applets used on this page

This page uses JSXGraph.

JSXGraph is a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser. It is implemented completely in JavaScript, does not rely on any other library. It uses SVG and VML and is fully HTML5 compliant.

This page also uses the MathJax system for displaying maths symbols.

JSXGraph is a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser. It is implemented completely in JavaScript, does not rely on any other library. It uses SVG and VML and is fully HTML5 compliant.

This page also uses the MathJax system for displaying maths symbols.

## Glossary

### composite

made of a combination of simpler shapes or bodies

### function

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

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AP Calculus AB (USA) | 3 | Differentiation | Rules |

AP Calculus BC (USA) | 3 | Differentiation | Rules |

AQA A-Level (UK - Pre-2017) | C3 | Differentiation | Rules |

AQA A2 Maths 2017 | Pure Maths | Differentiation | Using Differentiation Rules |

AQA AS/A2 Maths 2017 | Pure Maths | Differentiation | Using Differentiation Rules |

CBSE XI (India) | Calculus | Limits and Derivatives | Sum, difference, product and quotient rules |

CCEA A-Level (NI) | C3 | Differentiation | Rules |

CIE A-Level (UK) | P2 | Differentiation | Rules |

G Differentiation | G4 Differentiation Techniques | Using Differentiation Rules | |

Edexcel A-Level (UK - Pre-2017) | C3 | Differentiation | Rules |

Edexcel A2 Maths 2017 | Pure Maths | Differentiation | Using Differentiation Rules |

Edexcel AS/A2 Maths 2017 | Pure Maths | Differentiation | Using Differentiation Rules |

I.B. Higher Level | 6 | Differentiation | Rules |

I.B. Standard Level | 6 | Differentiation | Rules |

Methods (UK) | M8 | Differentiation | Rules |

OCR A-Level (UK - Pre-2017) | C3 | Differentiation | Rules |

OCR A2 Maths 2017 | Pure Maths | Differentiation Techniques | Using Differentiation Rules |

OCR MEI A2 Maths 2017 | Pure Maths | Differentiation Techniques | Using Differentiation Rules |

OCR-MEI A-Level (UK - Pre-2017) | C3 | Differentiation | Rules |

Pre-U A-Level (UK) | 4 | Differentiation | Rules |

Scottish Advanced Highers | M1 | Differentiation | Rules |

Scottish (Highers + Advanced) | AM1 | Differentiation | Rules |

Universal (all site questions) | D | Differentiation | Rules |

WJEC A-Level (Wales) | C3 | Differentiation | Rules |