Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.6 Exercises - Page 372: 42

Answer

$f'(x)= \frac{1}{|x|\sqrt{4x^2-1}}$

Work Step by Step

$f(x)=arcsec(2x)$ $let$ $u=2x, u'=2$ $\frac{d}{dx}(arcsecu)= \frac{u'}{|u|\sqrt{u^2-1}}$ $f'(x)= \frac{2}{|2x|\sqrt{4x^2-1}}$ $f'(x)= \frac{1}{|x|\sqrt{4x^2-1}}$
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