Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.6 - Derivatives of Logarithmic Functions - 3.6 Exercises - Page 223: 18


$y'=\csc x$

Work Step by Step

$y=\ln (\csc x-\cot x)\\ y'=\frac{1}{\csc x-\cot x} \times (-\cot x\csc x)-(-(\csc x)^2) \\ y'=\frac{1}{\csc x-\cot x} \times \csc ^{2} x-\cot x \csc x \\ y'=\frac{\csc x(\csc x-\cot x)}{\csc x-\cot x} \\ y'=\csc x$
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