hw10-3 - rules. unction Derivative ln x 1 x 1. rom Section...

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Math 170-010 Homework 10/3 Fall 2011 Goals: Compute the derivative of ln x the hard way. Compute lots of log derivatives the easy way. Work Type I and Type II problems. Warm Up: (If you didn’t do this in class.) 1. Assume y = x . (a) Square both sides. (Check your answer against mine.) (b) DiFerentiate both sides. (Check your answer against mine.) (c) Solve for y . (Check your answer against mine.) (d) Substitute y out of your answer. (Check your answer against mine.) 2. Assume y = ln x . (a) Exponentiate both sides. (Check your answer against mine.) (b) DiFerentiate both sides. (Check your answer against mine.) (c) Solve for y . (Check your answer against mine.) (d) Substitute y out of your answer. (Check your answer against mine.) Exercises: Assume that the following derivative has been added to the list of quick derivative
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Unformatted text preview: rules. unction Derivative ln x 1 x 1. rom Section 4.7 of the Online Textbook: Problems 11, 12, 13, 14, 16, 17, 18 and 21. 2. or the function f ( x ) = sin 2 x + x : (a) ind the tangent slope at x = 0. (b) Where in the interval [0 , 2 ] is the slope horizontal? 1 3. For the function f ( x ) = x ln x 2 : (a) Where is the slope horizontal? (b) Find the equation of the tangent line at x = 2. Challenge Problem: Online Textbook, Section 4.7: problem 20. Hints and Answers Warm Up: 1. (a) y 2 = x . (b) 2 yy = 1 (c) y = 1 2 y (d) y = 1 2 x 2. (a) e y = x (b) e y y = 1 (c) y = 1 e y (d) y = 1 x Exercises: 2. (a) 3 (b) 3 , 2 3 , 4 3 , 5 3 3. (a) x = e 1 . 368 (b) y = (2 + ln 4) x-4 3 . 386 x-4 2...
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This note was uploaded on 10/11/2011 for the course MATH 170 taught by Professor Staff during the Fall '08 term at Boise State.

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hw10-3 - rules. unction Derivative ln x 1 x 1. rom Section...

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