University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.3 - Differentiation Rules - Exercises: 53

Answer

a) 13 b) -7 c) $\frac{7}{25}$ d) 20

Work Step by Step

a) $\frac{d}{dx}uv =uv' +vu' = u(0)v'(0) +v(0)u'(0) = 5(2) -1(-3) = 13$ b) $\frac{d}{dx}(\frac{u}{v}) = \frac{v(0)u'(0) - u(0)v'(0)}{v(0)^{2}} = \frac{3-10}{1} = -7$ c) $\frac{d}{dx}(\frac{v}{u}) = \frac{u(0)v'(0) - v(0)u'(0)}{u(0)^{2}} = \frac{7}{25}$ d) $ \frac{d}{dx}(7v-2u) = 7v'(0)- 2u'(0)= 7(2)-2(-3)= 14+6= 20$
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