Answer
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Work Step by Step
Given the velocity $v(x)=f(x)$, we have $\frac{dv}{dx}=f'(x)$. With the relation $\frac{dx}{dt}=v=f(x)$, the acceleration is:
$a=\frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=f'(x)v=f'(x)f(x)$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 3: Derivatives - Section 3.6 - The Chain Rule - Exercises 3.6 - Page 150: 88
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