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 14.6 - Tangent Planes and Differentials - Exercises 14.6 - Page 835: 53


The function $f$ is more sensitive to a change in $d$.

Work Step by Step

$f (a,b,c,d)=ad-b c$ and $f_a=d \\ f_b=-c \\ f_c=-b \\ f_d=a$ $\implies df = d \ da -c \ db -b \ dc +a \ d \ d$ $\implies df=2 dx +1 dy$ So, we can see that as |a| is bigger than b, c and d, the function $f$ is more sensitive to a change in $d$.
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