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 147: 84


a) 36 b) 21 c) 58

Work Step by Step

a) $\frac{d}{dx}(f(x))^{3}|_{x=0}=3(f(0))^{2}\times f'(0)$ $=3(2)^{2}\times3=36$ b) $\frac{d}{dx}f(7x)|_{x=0}=f'(7\times0)\times\frac{d}{dx}(7x)$ $=3\times7=21$ c) $\frac{d}{dx}[f(4x)h(5x)]$ $=f'(4x)\times h(5x)+f(4x)\times h'(5x)$ Derivative at $x=0$ $=f'(4\times0)\times4\times h(5\times0)+ f(4\times0)\times h'(5\times0)\times5$ $=3\times4\times-1+2\times7\times5=-12+70=58$
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