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: 19


$$f_x= y\cos(xy)e^{-x-y}-\sin(xy)e^{-x-y},$$ $$f_y= x\cos(xy)e^{-x-y}-\sin(xy)e^{-x-y}.$$

Work Step by Step

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