What does $D_{12}f$ mean in the context of partial derivatives, with $f: \mathbb{R}^2 \to \mathbb{R}$, for example? This is used in Rudin's Principles of Mathematical Analysis.
It is clear to me what that $D_1 f$ is the partial derivative of $f$ with respect to $x$. Is $D_{12}f$ a row vector $ \begin{bmatrix} D_1f & D_2f \end{bmatrix} $?
No, usually $$ D_{12}f=\frac{\partial f}{\partial x\partial y}. $$