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This lecture from M.I.T. is 40-50 minutes long delivered by Professor David Jerison and covers exponential and logarithmic functions. It is aimed at undergraduate students.

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

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

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-