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: 20


$\dfrac{1}{x \ln y}$ and $\dfrac{-\ln x}{y(\ln y)^2}$

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: $f_x=\dfrac{1}{\ln y} \times \dfrac{\partial (\ln x)}{\partial x}=\dfrac{1}{x \ln y}$ $f_y=\ln (x) \times [(-\ln y)^2] \times \dfrac{\partial (\ln y)}{\partial y}=\dfrac{-\ln x}{y(\ln y)^2}$
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.