Thomas' Calculus 13th Edition

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

Chapter 14: Partial Derivatives - Practice Exercises - Page 864: 29



Work Step by Step

$x=e^{t}=1$ ($t=0$) $\frac{dx}{dt}=e^{t}=1$ ($t=0$) $y=\ln(t+1)=0$ ($t=0$) $\frac{dy}{dt}=\frac{1}{t+1}=1$ ($t=0$) $w=sin(xy+\pi)$ $w_{x}=y\times cos(xy+\pi)=0$ ($t=0$) $w_{y}=x\times cos(xy+\pi)=-1$ ($t=0$) $\frac{dw}{dt}=w_{x}\frac{dx}{dt}+w_{y}\frac{dy}{dt}=-1$ at $t=0$
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