Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises - Page 446: 36


$\csc x$

Work Step by Step

$\frac{d}{dx}\ln(\csc x-\cot x)$ $=\frac{1}{\csc x-\cot x}*\frac{d}{dx}(\csc x-\cot x)$ $=\frac{1}{\csc x-\cot x}*(-\csc x\cot x-(-\csc^2 x))$ $=\frac{1}{\csc x-\cot x}*(-\csc x\cot x+\csc^2 x)$ $=\frac{1}{\csc x-\cot x}*\csc x*(\csc x-\cot x)$ $=\csc x$
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