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: 19


$x^{y-1} \space y$ and $x^{y} \space \ln (x)$

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: $f_x=\dfrac{\partial (x^y)}{\partial x}=x^{y-1} \space y$ $f_y=\dfrac{\partial (x^y)}{\partial y}=x^{y} \space \ln (x)$
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