Answer
$y=2x-2$
Work Step by Step
The equation of the tangent line at $(1,0)$ is:
$$y=0+f'(1)(x-1)$$
Using the chain rule it follows:
$$f'(x)=\frac{2}{x}\cos(2\ln(x))$$
$$f'(1)=\frac{2}{1}\cos(2\ln(1))$$
$$f'(1)=2$$
so:
$$y=0+2(x-1)$$
$$y=2x-2$$
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises - Page 446: 47
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