lecture5Student.pdf - Lecture 5 Unit 4 Differentiation(continued Outline 1 Introduction 2 Examples 3 Economic Applications MR and MC 4 Conclusion

lecture5Student.pdf - Lecture 5 Unit 4...

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Lecture 5, Unit 4: Differentiation (continued) 18/2/2015
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Outline 1 Introduction 2 Examples 3 Economic Applications: MR and MC 4 Conclusion
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Literature Renshaw, ch. 6 & ch. 13 (13.2-13.3)
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Introduction Last time we encountered the rules of differentiation Today we’ll apply these rules to find the derivatives of some functions We’ll also introduce the marginal revenue and marginal cost functions
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Example 1 Suppose that y = (4 x 2 - 3)(2 x 5 + x ). Find dy dx
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Example 2 Suppose that y = x 2 +1 1 - x 2 . Find dy dx
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Example 3 Suppose that y = ( x 2 - 2 x 3 ) 5 . Find dy dx
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Example 4 Suppose that y = 1 e x . Find dy dx
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Example 5 Suppose that y = ln 1 x . Find dy dx
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Economic Applications Two frequently encountered applications derivatives are: Marginal revenue function Marginal cost function
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Marginal revenue, MR: p. 233 Recall that total revenue is R = pq We often have to multiply demand curve/function by p (alternatively, multiply inverse demand curve/function by q) to obtain total revenue function
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