Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.5 The Chain Rule - 14.5 Exercises - Page 985: 44

Answer

$4.65 Hz/s$ and $576.6$ Hz

Work Step by Step

We have the perceived frequency:$=( 460) [\dfrac{332+34}{332-40}]=576.6$ Hz Now, we have $\dfrac{d}{dt}[\dfrac{C+V_0}{C-f_s}f] =\dfrac{(C-f_s)(C+V_0)'-(C+V_0)(C-V_s)}{(C-f_s)^2}f$ We need to re-write the above equation as: $\dfrac{d}{dt}[\dfrac{C+V_0}{C-f_s}f] =\dfrac{(C-f_s)(V_0)'+(C+V_0)(V_s)}{(C-f_s)^2}f$ Now, substitute the given values, then we have: $\dfrac{(C-f_s)(V_0)'+(C+V_0)(V_s)}{(C-f_s)^2}f = ( 460)[\dfrac{(332-40)(1.2)+(332+34)(1.4)}{(332-40)^2}] \\ =4.65 Hz/s$
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