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: 75


$$\frac{d^3}{dx^3}(9-x)^8 = -336( 9-x)^5.$$

Work Step by Step

We have $$\frac{d}{dx}(9-x)^8=8( 9-x)^7(-1)=-8( 9-x)^7$$ and $$\frac{d^2}{dx^2}(9-x)^8 =-56( 9-x)^6(-1)=56( 9-x)^6.$$ Hence, $$\frac{d^3}{dx^3}(9-x)^8 = 56\frac{d}{dx}(( 9-x)^6\\ =336( 9-x)^5 (-1)=-336( 9-x)^5.$$
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