hw9-16 - Math 170-010 Homework 9/16 Fall 2011 Goal...

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Math 170-010 Homework 9/16 Fall 2011 Goal: Recognize which rule applies to what kind of function. Use the rules to compute derivatives. Exercises: Go to Schaum’s , Chapter 10. Each of Problems 32–45 requires either a product rule, a quotient rule, a chain rule, or perhaps more than one of these. For each problem state which rule you will use. If you will use more than one, state them in the order you plan to use them. Then compute the derivative. NOTE: there is more then one correct approach on many of these problems. I will give answers for my choice of rules and the unsimplified result. You might get a different, but still correct, answer. Challenge Problem: The graphs of a function, f , and its derivative, f , are shown at right. Suppose that g = f ( x 2 ) 1. Estimate f (4). 2. Find g 3. Estimate g (2). Hints and Answers 32. Chain. y = 6(1 - 5 x ) 5 ( - 5) 33. Chain. f = 4(3 x - x 3 + 1) 3 (3 - 3 x 2 ) 1
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34. Chain. y = 1 2 (3 + 4 x - x 2 ) 1 / 2 (4 - 2 x ) 35. Quotient. θ = (2 r + 3)(3) - (3 r + 2)(2) (2 r + 3) 2 36. Chain, then quotient. y = 5
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