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: 17


$$ R'(y) =\frac{-3+4\cos y}{\sin^2 y}.$$

Work Step by Step

Since $ R(y)= \frac{3\cos y-4}{\sin y}$, then using the quotient rule, the derivative is giving by $$ R'(y)=\frac{\sin y(-3\sin y)-\cos y(3\cos y-4)}{\sin^2 y} \\ =\frac{-3\sin^2 y-3\cos^2 y+4\cos y)}{\sin^2 y}\\ =\frac{-3+4\cos y}{\sin^2 y}.$$
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