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: 13

Answer

$p'(2)=42$

Work Step by Step

Notice that $g(t)=x $ and $h(t)=y$. We will use the Chain Rule to find $p'(t)$ and then find it for $t=2$: $$p'(t)=(f(g(t),h(t))'=f_x(g(t),h(t))g'(t)+f_y(g(t),h(t))h'(t)$$ So, $$p'(2)=f_x(g(2),h(2))g'(2)+f_y(g(2),h(2))h'(2)= f_x(4,5)\cdot(-3)+f_y(4,5)\cdot6=2\cdot(-3)+8\cdot6=42$$
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