Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 13 - Functions of Several Variables - 13.3 Exercises - Page 896: 12

Answer

$$\frac{\partial z}{\partial x}=\frac{y^2}{\sqrt x}$$ $$\frac{\partial z}{\partial y}=4y\sqrt x$$

Work Step by Step

The partial derivative with the respect to $x$ is: $$\frac{\partial z}{\partial x}=\frac{\partial }{\partial x}(2y^2\sqrt x)=2y^2\frac{\partial }{\partial x}(\sqrt x)=2y^2\cdot\frac{1}{2\sqrt x}=\frac{y^2}{\sqrt x}$$ because $y$ is treated as a constant. The partial derivative with the respect to $y$ is: $$\frac{\partial z}{\partial y}=\frac{\partial }{\partial y}(2y^2\sqrt x)=2\sqrt x\frac{\partial }{\partial y}(y^2)=2\sqrt x2y=4y\sqrt x$$ because now $x$ is treated as a constant.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.