$$ \gdef\pd#1#2{\frac{\partial #1}{\partial #2}}
\gdef\d#1{\, \mathrm{d}#1}
\gdef\dx{\d{x}}
\gdef\tr#1{\operatorname{tr} (#1)}
$$
$$
\gdef\norm#1{\left \lVert #1 \right\rVert}
\gdef\seminorm#1{| #1 |}
$$
$$
\gdef\vec#1{\mathbf{\boldsymbol{#1}}}
\gdef\dvec#1{\bar{\vec #1}}
$$