Answer
False.
Work Step by Step
$\frac{d}{dt}\left(\sqrt{f^2(t) + g^2(t)}\right) \neq \sqrt{(f'(t))^2 + (g'(t))^2}$. For instance, take $f(t) = \sin(t), g(t) = \cos(t)$.
Multivariable Calculus, 7th Edition
by Stewart, James
Published by
Brooks Cole
ISBN 10:
0-53849-787-4
ISBN 13:
978-0-53849-787-9
Chapter 13 - Vector Functions - Review - True-False Quiz - Page 897: 6
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