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: 32


$f_x=e^{-xyz}\times-yz$ $f_y=e^{-xyz}\times-xz$ $f_z=e^{-xyz}\times-xy$

Work Step by Step

Take the first partial derivatives of the given function. When taking a partial derivative with respect to x, treat y and z as constants, with respect to y, treat x and z as constants, and with respect to z, treat x and y as constants: $f_x=e^{-xyz}\times-yz$ $f_y=e^{-xyz}\times-xz$ $f_z=e^{-xyz}\times-xy$
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