Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.6 Exercises - Page 153: 8


a) $\frac{dy}{dt}=-2$ b) $\frac{dy}{dt}=-2\sqrt 2$ c) $\frac{dy}{dt}=-2\sqrt 3$

Work Step by Step

Using the chain rule, differentiate with respect to t. $$\frac{dy}{dt}=-sin(x)\times\frac{dx}{dt}$$ Plug in the known values of $\frac{dx}{dt}$ and x, then simplify. $$\frac{dy}{dt}=-4sin(\pi\div6)\\=-2$$ Plug in $\pi/4$ for b, to get $\frac{dy}{dt}=-4sin(\pi\div4)\\=-2\sqrt 2$ For part c, plug in $\pi/3$ for x to get $\frac{dy}{dt}=-4sin(\pi\div3)\\=-2\sqrt 3$
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