Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.6 Trigonometric Functions - Exercises - Page 140: 16


$$ G'(z)= -(\tan z -\cot z)^{-2}(\sec^2z+\csc^2 z).$$

Work Step by Step

Since $ G(z)= \frac{1}{\tan z -\cot z}$, rewriting $ G $ as follows $$ G(z)= (\tan z -\cot z)^{-1}.$$ Now, the derivative is giving by $$ G'(z)= -(\tan z -\cot z)^{-2}(\sec^2z+\csc^2 z).$$
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