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: 7


a) $2xsin(9-x^2)$ b)$x^{-2}sin(x^{-1})$ c)$-sec^2xsin(tanx)$

Work Step by Step

a) $u(x) = 9-x^2$ $\frac{d}{dx}cos(9-x^2)$ $=u'(x)cos'(9-x^2)$ $=(-2x)(-sin(9-x^2))$ $=2xsin(9-x^2)$ b) $u(x) = x^{-1}$ $\frac{d}{dx}cos(x^{-1})$ $=u'(x)cos'(x^{-1})$ $=(-x^{-2})(-sin(x^{-1}))$ $=x^{-2}sin(x^{-1})$ c) $u(x) = tanx$ $\frac{d}{dx}cos(tanx)$ $=u'(x)cos'(tanx)$ $=sec^2x(-sin(tanx))$ $=-sec^2xsin(tanx)$
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.