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 - Page 125: 12


The derivative is $\frac{-tsin(t)-3cos(t)}{t^4}$

Work Step by Step

Using the quotient rule: $f'(t)=(\frac{u(t)}{v(t)})'=\frac{u'(t)v(t)-v'(t)u(t)}{(v(t))^2}$ $u(t)=cos(t) ;u'(t)=-sin(t)$ $v(t)=t^3 ;v'(t)=3t^2$ $f'(t)=\frac{(-sin(t))(t^3)-(cos(t))(3t^2)}{(t^3)^2}$ $=\frac{(t^2)(-tsin(t)-3cos(t))}{t^6}=\frac{-tsin(t)-3cos(t)}{t^4}$.
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