I am given a 3 variable function: f(x,y,z)=cos(xy)+cos(yz)+cos(zx) How to do the Hessian matrix for a 3 variable function.

I am given a $3$ variable function:
$f\left(x,y,z\right)=\mathrm{cos}\left(xy\right)+\mathrm{cos}\left(yz\right)+\mathrm{cos}\left(zx\right)$
How to do the Hessian matrix for a $3$ variable function.
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Isabella Rocha
Notice that since $\mathrm{cos}\left(w\right)\le 1$, hence $f\left(x,y,z\right)\le 3$.
Also note that $f\left(0,0,0\right)=3$, hence $\left(0,0,0\right)$ must be a global maximum.
No computation of hessian is needed.
Remark:
The hessian is the matrix $\left[\begin{array}{ccc}{f}_{xx}& {f}_{xy}& {f}_{xz}\\ {f}_{yx}& {f}_{yy}& {f}_{yz}\\ {f}_{zx}& {f}_{zy}& {f}_{zz}\end{array}\right]$