= Solution
Write $D_x=y\partial_z-z\partial_y$, $D_y=z\partial_x-x\partial_z$ and $D_z=x\partial_y-y\partial_x$. The <product rule> applied to a smooth test <function> $f$ gives
$$
[D_x,D_y]f=y\partial_xf-x\partial_yf=-D_zf.
$$
The mixed second <partial derivatives> cancel because they commute. Since the <orbital angular momentum> components are $\hat j_i=-i\hbar D_i$, their <commutator> is
$$
\boxed{[\hat j_x,\hat j_y]=(-i\hbar)^2(-D_z)=i\hbar\hat j_z.}
$$
This is one of the <orbital angular momentum commutation relations>; the <Planck constant> enters through the definition of each <linear operator>.
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