Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - 14.3 Partial Derivatives - 14.3 Exercises: 28

Answer

$$\frac{\partial}{\partial x}f(x,y)=yx^{y-1}$$ $$\frac{\partial}{\partial y}f(x,y)=x^y\ln x$$

Work Step by Step

Regard $y$ as constant and differentiate with respect to $x$. Then $f$ is treated as a simpe power function: $$\frac{\partial}{\partial x}f(x,y)=\frac{\partial}{\partial x}x^y=yx^{y-1}.$$ Regard $x$ as constrant and differentiate with respect to $y$. Then $f$ is treated as a simpe exponential function: $$\frac{\partial}{\partial y}f(x,y)=\frac{\partial}{\partial y}x^y=x^y\ln x.$$
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