Thomas' Calculus 13th Edition

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

Chapter 14: Partial Derivatives - Section 14.4 - The Chain Rule - Exercises 14.4 - Page 816: 1


a. $0$ b. $0$

Work Step by Step

a. Using chain rule: $\dfrac{dw}{dt}=\dfrac{\partial w}{\partial x}\dfrac{dx}{dt}+\dfrac{\partial w}{\partial y}\dfrac{dy}{dt}=-2x \sin t+2y \cos t$ and, $-2\cos t \sin t+2 \sin t \cos t=0$ b. Using direct differentiation: we have $w^2=x^2+y^2=\cos^2 t+\sin^2 t=1$ and $\dfrac{dw}{dt}=0$ Then, $\dfrac{dw}{dt}(\pi)=0$
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