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Chapter 2, Essence of calculus
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Essence of calculus, chapter 2
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Outro
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Essence of calculus E2
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Intro
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Essence of calculus chapter 2
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f(x) = x^2
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f(x) = x^3
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Sine
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Sum rule
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Product rule
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Chain rule
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Motivating example
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Deriving the key proportionality property
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What is e?
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Natural logs
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Writing e^ct is a choice
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Opening circle example
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Ladder example
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Implicit differentiation intuition
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Derivative of ln(x)
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Formal definition of derivatives
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Epsilon delta definition
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L'Hôpital's rule
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Car example
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Areas under graphs
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Fundamental theorem of calculus
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Recap
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Negative area
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Approximating cos(x)
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Generalizing
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e^x
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Geometric meaning of the second term
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Convergence issues
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The transformational view of derivatives
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An infinite fraction puzzle
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Cobweb diagrams
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Stability of fixed points
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Why learn this?
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