TITLE: What do you call a function differentiated with respect to all of its arguments?
QUESTION [5 upvotes]: Just a simple question. 
Let $f(x_1, x_2, \ldots, x_n)$ be a smooth function. Is there a particular name for the function
$$\frac{\partial^n f}{\partial x_1 \, \partial x_2 \cdots \partial x_n}$$

REPLY [3 votes]: This does not have a name. We call it the $n$-th partial difference of $f$ w.r.t. the vector $x$ or variables $x_1$, $x_2$, ..., $x_n$.