Math150Sols7S11

Math150Sols7S11 - QUIZ ON CHAPTER 7 SOLUTIONS MATH 150...

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QUIZ ON CHAPTER 7 SOLUTIONS MATH 150 – SPRING 2011 – KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% Show all work, simplify as appropriate, and use “good form and procedure” (as in class). Box in your final answers! No notes or books allowed. A scientific calculator is allowed. 1) Find the following derivatives. Simplify completely unless you are told not to. (61 points total) a) D w ln sin 4 w () ± ² ³ ´ (6 points) = 1 sin 4 w ± D w sin 4 w ² ³ ´ µ = 1 sin 4 w ± cos 4 w ² ³ ´ µ ± 4 ² ³ ´ µ = 4cot 4 w b) D x log 9 5 x 2 ± x + 3 [] (6 points) = D x ln 5 x 2 ± x + 3 ln9 ² ³ ´ ´ µ · · by the Change-of-Base Property of Logs = 1 ¸ D x ln 5 x 2 ± x + 3 ² ³ µ = 1 ¸ 1 5 x 2 ± x + 3 ¸ D x 5 x 2 ± x + 3 = 1 ¸ 1 5 x 2 ± x + 3 ¸ 10 x ± 1 = 10 x ± 1 5 x 2 ± x + 3
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c) D x e 5 x ln x () 3 ± ² ³ ´ µ (8 points) You do not have to write your final answer as a single fraction. Use the Product Rule for Derivatives. = D x e 5 x ± ² ³ ´ µ ln x 3 ± ² ³ ´ · + e 5 x ± ² ³ ´ µ D x ln x 3 ± ² ³ ´ · = 5 e 5 x ± ² ³ ´ µ ln x 3 ± ² ³ ´ · + e 5 x ± ² ³ ´ µ 3ln x 2 µ D x ln x ± ² ³ ´ · = 5 e 5 x ln x 3 + e 5 x ± ² ³ ´ µ x 2 µ 1 x ± ² ³ ´ · = 5 e 5 x ln x 3 + 3 e 5 x ln x 2 x , or 5 xe 5 x ln x 3 + 3 e 5 x ln x 2 x , or e 5 x ln x 2 5 x ln x + 3 ± ² ³ ´ x d) D x 3 x + 7 6 x 2 ± 3 4 2 x + 9 7 ² ³ ´ ´ ´ µ · · · You must use logarithmic differentiation and apply appropriate laws of logarithms whenever they apply, as we have done in class. You do not
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This note was uploaded on 09/08/2011 for the course MATH 150 taught by Professor Bart during the Spring '06 term at Mesa CC.

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Math150Sols7S11 - QUIZ ON CHAPTER 7 SOLUTIONS MATH 150...

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