Similar to Einstein, many applied math papers use the notation "$\partial$" as the gradient operator. For example, $\partial f(x)$ means the gradient of $f$ at $x$.
$x$ is a vector.
In my paper I need to use both partial derivative and gradient. For example, consider the following three equivalent expressions:
$\frac{\partial\partial f(x)}{\partial x_i}$
$\partial_{x_i}\partial f(x)$
$\partial_{x_i}\nabla f(x)$
Will the first express cause any ambiguity to readers as the two "$\partial$" symbols have different meanings? Which expression is the least ambiguous one?
You are welcome to supply your own favorite notation, too. Thanks in advance!
An alternative is to use the subscript after the comma $_{,\ i}$ to denote (partial) differentiation wrt $x_i$. So, e.g., $$\partial f_{ij,\ k}=\frac{\partial}{\partial x_{k}}(\partial f_{ij})\ .$$