Number of Partial Derivatives of Order n/Examples/Order n of 2 Variables

Examples of Use of Number of Partial Derivatives of Order $n$
Let $u = \map f {x, y}$ be a real function of $2$ variables.

There are $2^n$ partial derivatives of $u$ of order $n$.

Proof
From Number of Partial Derivatives of Order $n$, there are $m^n$ partial derivatives of order $n$ of a function of $m$ independent variables.

In this case, $m = 2$.

Thus there are $2^n$ partial derivatives of $u$ of order $n$.