Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 13 - Partial Derivatives - 13.1 Functions Of Two Or More Variables - Exercises Set 13.1: 3

Answer

(a) $f(x+y,x-y)=x^2-y^2+3$, (b) $f(xy,3x^2y^3)=3(x^3y^4+1)$

Work Step by Step

(a) Substitute $x=x+y$ and $y=x-y:$ $$f(x+y,x-y)=(x+y)(x-y)+3=x^2-y^2+3$$ (b) Substitute $x=xy$ and $y=3x^2y^3:$ $$f(xy,3x^2y^3)=xy\cdot3x^2y^3+3=3(x^3y^4+1)$$
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