Chapter 14: Partial Derivatives - Section 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 14

$f_x=e^{-x}cos(x+y)-e^{-x}sin(x+y)$ $f_y=e^{-x}cos(x+y)$

Take the first partial derivatives of the given function. When taking a partial derivative with respect to x, treat y as a constant, and vice versa: $f_x=e^{-x}cos(x+y)-e^{-x}sin(x+y)$ $f_y=e^{-x}cos(x+y)\times1$