Chapter 12 - Functions of Several Veriables - 12.4 Partial Derivatives - 12.4 Exercises - Page 904: 48

$Q_{x}(x,y,z)=yz \sec^{2} xyz$ $Q_{y}(x,y,z)=xz\sec^{2} xyz$ $Q_{z}(x,y,z)=xy\sec^{2} xyz$

Treating $yz$ as a constant and differentiating with respect to $x$, we have $Q_{x}(x,y,z)=yz \sec^{2} xyz$ Holding $xz$ fixed and differentiating with respect to $y$, we get $Q_{y}(x,y,z)=xz\sec^{2} xyz$ Holding $xy$ fixed and differentiating with respect to $z$, we get $Q_{z}(x,y,z)=xy\sec^{2} xyz$