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: 41

Answer

$f'(t)=\frac{-t\sin(t)-\cos(t)}{t^2}$.

Work Step by Step

Using the quotient rule: $g'(t)=(\frac{u(t)}{v(t)})'=\frac{u'(t)v(t)-v'(t)u(t)}{(v(t))^2}$. $u(t)=\cos(t) ;u'(t)=-\sin(t)$. $v(t)=t ;v'(t)=1$. $f'(t)=\frac{(-\sin(t))(t)-(1)(\cos(t))}{t^2}$. $=\frac{-t\sin(t)-\cos(t)}{t^2}$.
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