Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 13 - Review - Concept Check - Page 881: 4

Answer

a) See the explanation. b) See the explanation. c) See the explanation. d) See the explanation. e) See the explanation. f) See the explanation.

Work Step by Step

a) $u(t)+v(t)=\frac{d}{dt}[u(t)+v(t)]=u'(t)+v'(t)$ It is known as the sum rule of differentiation. b) $cu(t)=\frac{d}{dt}[cu(t)]=cu'(t)$ It is known as the scalar multiple rule of differentiation. (c) $f(t) v(t)=\frac{d}{dt}[f(t)u(t)]=f'(t)u(t)+f(t)u'(t)$ It is known as the product rule of differentiation. d) $u(t) \cdot v(t)=\frac{d}{dt}[u(t) \cdot v(t)]=u'(t) \cdot v(t)+u(t) \cdot v'(t)$ It is known as the dot product rule of differentiation. e) $u(t) \times v(t)=\frac{d}{dt}[u(t) \times v(t)]=u'(t) \times v(t)+u(t) \times v'(t)$ It is known as the cross product rule of differentiation. f) $\frac{d}{dt}[u(f(t))]=f'(t)u'(f(t))$ It is known as the chain rule of differentiation.
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