= Solution
The <chain rule> gives
$$
\frac\partial{\partial x'^\alpha}
=\frac{\partial x^\beta}{\partial x'^\alpha}\frac\partial{\partial x^\beta}.
$$
Thus
$$
\boxed{\partial_\alpha\equiv\frac\partial{\partial x^\alpha}\text{ transforms covariantly}.}
$$
Differentiation with respect to a contravariant coordinate has a lower transformation index. In inertial Cartesian coordinates in <Minkowski spacetime>, no connection term is needed for this coordinate transformation of a derivative acting on a scalar; Lorentz transformations have constant Jacobians.
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