Calculus 10th Edition

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

Chapter 2 - Differentiation - 2.4 Exercises - Page 136: 58


$h(t)=-4\pi\csc^2{(\pi t+2)}\cot{(\pi t +2)}.$

Work Step by Step

$u=\cot{(\pi t+2)}$; $\dfrac{du}{dt}=-\pi\csc^2{(\pi t+2)}$ $h(u)=2u^2;\dfrac{d}{du}h(u)=4u$ $\dfrac{d}{dt}h(t)=\dfrac{d}{du}h(u)\times\dfrac{du}{dt}=(-\pi\csc^2{(\pi t+2)})(4\cot{(\pi t +2)})$ $=-4\pi\csc^2{(\pi t+2)}\cot{(\pi t +2)}.$
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