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

Summary/Background

graphic calculatorA note about graphic calculators
higher derivatives1st 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.

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.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopic
AP Calculus AB (USA)3DifferentiationRules
AP Calculus BC (USA)3DifferentiationRules
AQA A-Level (UK - Pre-2017)C3DifferentiationRules
AQA A2 Maths 2017Pure MathsDifferentiationUsing Differentiation Rules
AQA AS/A2 Maths 2017Pure MathsDifferentiationUsing Differentiation Rules
CBSE XI (India)CalculusLimits and DerivativesSum, difference, product and quotient rules
CCEA A-Level (NI)C3DifferentiationRules
CIE A-Level (UK)P2DifferentiationRules
G DifferentiationG4 Differentiation TechniquesUsing Differentiation Rules
Edexcel A-Level (UK - Pre-2017)C3DifferentiationRules
Edexcel A2 Maths 2017Pure MathsDifferentiationUsing Differentiation Rules
Edexcel AS/A2 Maths 2017Pure MathsDifferentiationUsing Differentiation Rules
I.B. Higher Level6DifferentiationRules
I.B. Standard Level6DifferentiationRules
Methods (UK)M8DifferentiationRules
OCR A-Level (UK - Pre-2017)C3DifferentiationRules
OCR A2 Maths 2017Pure MathsDifferentiation TechniquesUsing Differentiation Rules
OCR MEI A2 Maths 2017Pure MathsDifferentiation TechniquesUsing Differentiation Rules
OCR-MEI A-Level (UK - Pre-2017)C3DifferentiationRules
Pre-U A-Level (UK)4DifferentiationRules
Scottish Advanced HighersM1DifferentiationRules
Scottish (Highers + Advanced)AM1DifferentiationRules
Universal (all site questions)DDifferentiationRules
WJEC A-Level (Wales)C3DifferentiationRules