University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 3 - Practice Exercises - Page 202: 16



Work Step by Step

Given that $s=\csc^5(1-t+3t^2)$ Apply derivative rules of differentiation: $f(x)=p'(x)q(x)+p(x)q'(x)$ $y'=\dfrac{d}{dx}[\csc^5(1-t+3t^2)]$ $=5\csc^4(1-t+3t^2)\dfrac{d}{dx}(\csc(1-t+3t^2))$ $=5\csc^4(1-t+3t^2)(-csc(1-t+3t^2))(1-t+3t^2)\dfrac{d}{dx}((1-t+3t^2))$ $=5\csc^4(1-t+3t^2)(-csc(1-t+3t^2))(1-t+3t^2)(-1+6t)$ Hence, $s'=-5\csc^5(1-t+3t^2)cot(1-t+3t^2)(-1+6t)$
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