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: 26


$y'=2x \cot(5x)-5x^2 csc^2(5x)$

Work Step by Step

Given that $y=x^2 \cot 5x$ Apply derivative rules of differentiation: $f(x)=p'(x)q(x)+p(x)q'(x)$ $y'=\dfrac{d}{dx}[x^2 \cot 5x]$ $=2x \cot 5x-x^2 csc^2(5x) \dfrac{d}{dx}[5x]$ $=2x \cot(5x)-5x^2 csc^2(5x)$ Hence, $y'=2x \cot(5x)-5x^2 csc^2(5x)$
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