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This lecture from M.I.T. is 40-50 minutes long delivered by Professor David Jerison and covers the chain rule and higher derivatives. It is aimed at undergraduate students.

These lectures will give you some idea of how this subject is treated at university level.

Software/Applets used on this page

Video from MIT
Free lecture notes, exams, and videos are available from Massachusetts Institute of Technology at MIT. No registration required.

Glossary

chain rule

A rule for differentiating a function of a function:
dy/dx = dy/du x du/dx.

rule

A method for connecting one value with another.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AP Calculus AB (USA)3DifferentiationXTRA-
AP Calculus BC (USA)3DifferentiationXTRA-
AQA A-Level (UK - Pre-2017)C3DifferentiationXTRA-
AQA A2 Maths 2017Pure MathsDifferentiationExtra-
AQA AS/A2 Maths 2017Pure MathsDifferentiationExtra-
CCEA A-Level (NI)C3DifferentiationXTRA-
CIE A-Level (UK)P2DifferentiationXTRA-
Edexcel A-Level (UK - Pre-2017)C3DifferentiationXTRA-
Edexcel A2 Maths 2017Pure MathsDifferentiationExtra-
Edexcel AS/A2 Maths 2017Pure MathsDifferentiationExtra-
I.B. Higher Level6DifferentiationXTRA-
I.B. Standard Level6DifferentiationXTRA-
Methods (UK)M8DifferentiationXTRA-
OCR A-Level (UK - Pre-2017)C3DifferentiationXTRA-
OCR A2 Maths 2017Pure MathsDifferentiation TechniquesExtra-
OCR MEI A2 Maths 2017Pure MathsDifferentiation TechniquesExtra-
OCR-MEI A-Level (UK - Pre-2017)C3DifferentiationXTRA-
Pre-U A-Level (UK)4DifferentiationXTRA-
Scottish Advanced HighersM1DifferentiationXTRA-
Scottish (Highers + Advanced)AM1DifferentiationXTRA-
Universal (all site questions)DDifferentiationXTRA-
WJEC A-Level (Wales)C3DifferentiationXTRA-