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 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 3


a) $2x(y+2)$ b) $x^2-1$

Work Step by Step

a) Apply the chain rule as follows: $∂f/∂x = (x^2-1)'(y+2) + (x^2-1)(y+2)'= 2x (y +2) + (x^2-1)(0)= 2x(y+2)$ b) Apply the chain rule as follows: $∂f/∂y = (x^2-1)'(y+2) + (x^2-1)(y+2)'= 0(y+2) + (x^2-1)(1)= x^2-1$
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