Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises: 53

Answer

$y=2x+1$

Work Step by Step

The slope of the tangent can be calculated by taking first derivative of the function $y=e^{2x}cos\pi x$ $y'=e^{2x}\frac{d}{dx}(cos\pi x)+cos\pi x\frac{d}{dx}(e^{2x})$ $y'=2cos\pi x(e^{2x})-\pi (e^{2x})sin\pi x$ Slope of the tangent at (0,1) is given as follows: $y'|_{(0,1)}=2$ The equation of tangent at (0, 1) is $(y-1)=2(x-0)$ Hence, $y=2x+1$
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