Calculus 10th Edition

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

Chapter 2 - Differentiation - 2.3 Exercises: 61

Answer

$h'(\pi)=\dfrac{1}{\pi^2}$

Work Step by Step

Using the quotient rule: $h'(t)=(\frac{u(t)}{v(t)})'=\frac{u'(t)v(t)-v'(t)u(t)}{(v(t))^2}$. $u(t)=\sec(t) ;u'(t)=\sec(t)\tan(t)$. $v(t)=t ;v'(t)=1$ $h'(t)=\frac{(\sec(t)\tan(t))(t)-\sec(t)}{t^2}$. To evaluate, substitute $x=\pi$ : $h'(\pi)=\frac{\sec(\pi)((\pi)(\tan(\pi)-1)}{\pi^2}=\frac{1}{\pi^2}$.
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