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How fast are you really going?
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The gradient of secants and tangents to a graph
Calculating the gradient of
y
= x²
Definition of the derivative
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Some derivatives
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Introduction to differential calculus
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Motivation and knowledge
Calculus: Module 10
Introduction to differential calculus
Knowledge
Motivation - How fast are you really going?
Motivation - The more things change
Content - The gradient of secants and tangents to a graph
Content - Calculating the gradient of y = x²
Content - Definition of the derivative
Content - Notation for the derivative
Content - Some derivatives
Content - Properties of the derivative
Content - The product, quotient and chain rules
Content - Summary of differentiation rules
Content - The tangent line to a graph
Content - The second derivative
Content - Differentiation of inverses
Content - Implicit differentiation
Links forward - Higher derivatives
Links forward - Approximations of functions
History and applications - The discoverers of calculus
History and applications - The Newton–Leibniz controversy
History and applications - Mathematically rigorous calculus
Appendix
Answers to exercises
References
