Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - Chapter Review Exercises - Page 835: 20


$$f_x= \frac{2x+y^2}{x^2+xy^2},f_y= \frac{2xy}{x^2+xy^2}.$$

Work Step by Step

To calculate the partial derivatives, treat all variables as constant except the variable we are deriving with respect to. Since $f(x,y)=\ln(x^2+xy^2)$, then we have $$f_x=\frac{\partial f}{\partial x}=\frac{2x+y^2}{x^2+xy^2}$$ $$f_y=\frac{\partial f}{\partial y}=\frac{2xy}{x^2+xy^2}$$
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