University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.5 - Derivatives of Trigonometric Functions - Exercises: 21

Answer

$\displaystyle s' = \frac{-2\csc{t}\ \cot{t}}{(1-\csc{t})^{2}}$

Work Step by Step

$\displaystyle s = \frac{1+cosect}{1-cosect}$ $\displaystyle s' = \frac{-(1-cosect)cosect\ cot t - (1+cosect)cosect\ cott}{(1-cosect)^{2}}$ $\displaystyle s' = \frac{-cosect\ cott+cosec^{2}t\ cott -cosect\ cott-cosec^{2}t\ cott}{(1-cosect)^{2}}$ $\displaystyle s' = \frac{-2cosect\ cott}{(1-cosect)^{2}}$
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