Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.8 - Related Rates - Exercises 3.8 - Page 161: 4


$\dfrac{dx}{dt} = 3$

Work Step by Step

Given: $\dfrac{dy}{dt}=-2$ and $2x+3y=12$ Thus,on differentiating $y$ with respect to time, we get $\dfrac{d(2x+3y)}{dt}$ = $\frac{d (12)}{dt}$ or, $2\dfrac{dx}{dt} + 3\dfrac{dy}{dt}=0$ or, $2\dfrac{dx}{dt} = (-3)(-2)$ Thus, the answer is :$\dfrac{dx}{dt} = 3$
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