Chapter 14: Partial Derivatives - Section 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 32

$f_x=e^{-xyz}\times-yz$ $f_y=e^{-xyz}\times-xz$ $f_z=e^{-xyz}\times-xy$

Take the first partial derivatives of the given function. When taking a partial derivative with respect to x, treat y and z as constants, with respect to y, treat x and z as constants, and with respect to z, treat x and y as constants: $f_x=e^{-xyz}\times-yz$ $f_y=e^{-xyz}\times-xz$ $f_z=e^{-xyz}\times-xy$