Solution
= Solution
Under an orthogonal Cartesian change $x'_i=R_{ij}x_j$, the <chain rule> gives $\partial'_i=(\partial x_j/\partial x'_i)\partial_j=R_{ij}\partial_j$. Thus the derivative operator transforms as a rank-one <Cartesian tensor>. Under a general coordinate change it has the covector transformation law when applied to a scalar; derivatives of vector components then need the usual connection terms. The calculations below use Cartesian coordinates.