Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.4 - The Chain Rule - 3.4 Exercises - Page 205: 58

Answer

(a) $f(x) = sin(x+sin~2x)$ We can use the graph of $f(x)$ to make a sketch of $f'(x)$ (b) $f'(x) = cos(x+sin~2x)~(1+2~cos~2x)$
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Work Step by Step

(a) $f(x) = sin(x+sin~2x)$ We can use the graph of $f(x)$ to make a sketch of $f'(x)$ Note that $f'(x)$ has negative values when the slope of $f(x)$ has a negative slope, $f'(x)$ is 0 when the slope of $f(x)$ is 0, and $f'(x)$ has positive values when the slope of $f(x)$ has a positive slope. (b) $f'(x) = cos(x+sin~2x)\cdot \frac{d}{dx}(x+sin~2x)$ $f'(x) = (1+2~cos~2x)\cdot cos(x+sin~2x)$ We can use a graphing calculator to graph $f'(x)$ and compare it to our sketch in part (a)
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