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: 21


$-g(x)$ and $g(y)$

Work Step by Step

We need to take the first partial derivatives of the given function. In order to find the partial derivative we will differentiate with respect to $x$, by keeping $y$ as a constant, and vice versa: $f_x=\int_x^ y g(t) dt =- \int_{y}^{x} g(t) dt=\dfrac{\partial f}{\partial x}=-g(x)$ $f_y=\int_x^ y g(t) dt =\dfrac{\partial f}{\partial y}=g(y)$
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