Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 146: 61


$$ y'= -35x^4\cot^6(x^5)\csc^2( x^5).$$

Work Step by Step

Since $ y=\cot^7x^5$, by using the chain rule: $(f(g(x)))^{\prime}=f^{\prime}(g(x)) g^{\prime}(x)$ and recalling that $(\cot x)'=-\csc^2 x $, the derivative $ y'$ is given by $$ y'=7\cot^6x^5 (\cot x^5)'=7\cot^6x^5 (-\csc^2 x^5)( x^5)' \\=7\cot^6x^5 (-\csc^2 x^5)(5x^4)=-35x^4\cot^6(x^5)\csc^2( x^5).$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.