derivatives
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Examples using the Chain Rule.
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Even more examples using the chain rule.
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The product rule. Examples using the Product and Chain rules.
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Why the quotient rule is the same thing as the product rule. Introduction to the derivative of e^x, ln x, sin x, cos x, and tan x.
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More examples of taking derivatives.
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Half a century before direct experimental observation became possible, most structures of organic molecules were assigned by inspired guessing based on plausibility. But Wilhelm Körner developed a strictly logical system for proving the structure of benzene and its derivatives based on isomer counting and chemical transformation. His proof that the six hydrogen positions in benzene are equivalent is the outstanding example of this chemical...more
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Chain rule using partial derivatives (not a proof; more intuition).
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Financial institutions are a pillar of civilized society, supporting people in their productive ventures and managing the economic risks they take on. The workings of these institutions are important to comprehend if we are to predict their actions today and their evolution in the coming information age. The course strives to offer understanding of the theory of finance and its relation to the history, strengths and imperfections of such i...more
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Graphing functions using derivatives.
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Using the first and second derivatives to identify critical points and inflection points and to graph the function.
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Using derivatives to solve rate-of-change problems.
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Intuition on what happens to the slope/derivative and second derivatives at local maxima and minima.
